diff --git a/pages/Conquering Etiwanda Climb.md b/pages/Conquering Etiwanda Climb.md
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--- a/pages/Conquering Etiwanda Climb.md
+++ b/pages/Conquering Etiwanda Climb.md
@@ -1 +1,4337 @@
-- 020192
\ No newline at end of file
+- 020192
+- # Cycling pacing strategy calculation
+
+ **Created:** 12/11/2025 13:35:31
+ **Updated:** 12/11/2025 13:46:57
+ **Exported:** 12/11/2025 14:26:52
+ **Link:** [https://claude.ai/chat/64289705-d0c1-4f03-9139-a13815bc3969](https://claude.ai/chat/64289705-d0c1-4f03-9139-a13815bc3969)
+- ## Prompt:
+ 12/11/2025, 1:35:34 PM
+
+ 
+
+ use the formulas on https://www.gribble.org/cycling/power_v_speed.html to calculate a pacing strategy on the ride in the charts
+
+ rider weight - 203lbs
+ bike - 22lbs
+ gearing 38/20 (singlespeed)
+ target time 15:08
+- ## Response:
+ 12/11/2025, 1:36:47 PM
+
+ I'll fetch the formulas from that page and create a pacing strategy for your ride.
+
+ ````plaintext
+ Web Fetch: Fetched: An interactive model-based calculator of cycling power vs. speed
+ ````
+
+ Now I'll create a pacing strategy calculator using those formulas. Looking at your elevation profile, this is a climbing time trial with significant elevation gain (738 ft over 2.8 miles).
+
+ **Climb Pacing Strategy Calculator**
+
+ ````jsx
+ import React, { useState, useMemo } from 'react';
+ import { LineChart, Line, XAxis, YAxis, CartesianGrid, Tooltip, Legend, ResponsiveContainer } from 'recharts';
+
+ const ClimbPacingCalculator = () => {
+ const [params, setParams] = useState({
+ riderWeight: 203,
+ bikeWeight: 22,
+ CdA: 0.388, // Reasonable default for road position
+ Crr: 0.004, // Good tires on smooth pavement
+ drivetrainLoss: 2,
+ headwind: 0,
+ rho: 0.075, // Air density at sea level (lb/ft^3)
+ targetTime: 908 // 15:08 in seconds
+ });
+
+ // Convert elevation profile from image to data points
+ const elevationProfile = useMemo(() => {
+ const points = [];
+ const distances = [0, 0.2, 0.4, 0.6, 0.8, 1.0, 1.2, 1.4, 1.6, 1.8, 2.0, 2.2, 2.4, 2.6, 2.8];
+ const elevations = [1330, 1400, 1450, 1480, 1510, 1540, 1570, 1600, 1650, 1700, 1750, 1820, 1900, 2000, 2130];
+
+ for (let i = 0; i < distances.length; i++) {
+ const grade = i > 0
+ ? ((elevations[i] - elevations[i-1]) / (5280 * (distances[i] - distances[i-1]))) * 100
+ : 0;
+ points.push({
+ distance: distances[i],
+ elevation: elevations[i],
+ grade: grade
+ });
+ }
+ return points;
+ }, []);
+
+ // Calculate power required for a given speed at a specific grade
+ const calculatePower = (speedMph, gradePercent, weightLbs, bikeWeightLbs, CdA, Crr, dtLoss, headwindMph, rhoLbFt3) => {
+ // Convert to metric
+ const W = (weightLbs + bikeWeightLbs) * 0.453592; // kg
+ const Vgs = speedMph * 0.44704; // m/s
+ const Vhw = headwindMph * 0.44704; // m/s
+ const G = gradePercent;
+ const rho = rhoLbFt3 * 16.0185; // kg/m^3
+ const CdAMetric = CdA * 0.092903; // m^2
+
+ // Calculate forces
+ const Fgravity = 9.8067 * Math.sin(Math.atan(G / 100)) * W;
+ const Frolling = 9.8067 * Math.cos(Math.atan(G / 100)) * W * Crr;
+ const Vas = Vgs + Vhw;
+ const Fdrag = 0.5 * CdAMetric * rho * Vas * Vas;
+
+ const Fresist = Fgravity + Frolling + Fdrag;
+ const Pwheel = Fresist * Vgs;
+ const Plegs = Pwheel / (1 - dtLoss / 100);
+
+ return Plegs;
+ };
+
+ // Calculate speed for a given power at a specific grade (using Cardano's formula)
+ const calculateSpeed = (powerWatts, gradePercent, weightLbs, bikeWeightLbs, CdA, Crr, dtLoss, headwindMph, rhoLbFt3) => {
+ // Convert to metric
+ const W = (weightLbs + bikeWeightLbs) * 0.453592; // kg
+ const Vhw = headwindMph * 0.44704; // m/s
+ const G = gradePercent;
+ const rho = rhoLbFt3 * 16.0185; // kg/m^3
+ const CdAMetric = CdA * 0.092903; // m^2
+ const P = powerWatts;
+
+ // Cubic equation coefficients
+ const a = 0.5 * CdAMetric * rho;
+ const b = Vhw * CdAMetric * rho;
+ const c = (9.8067 * W * (Math.sin(Math.atan(G / 100)) + Crr * Math.cos(Math.atan(G / 100)))) +
+ (0.5 * CdAMetric * rho * Vhw * Vhw);
+ const d = -(1 - dtLoss / 100) * P;
+
+ // Cardano's formula
+ const Q = (3 * a * c - b * b) / (9 * a * a);
+ const R = (9 * a * b * c - 27 * a * a * d - 2 * b * b * b) / (54 * a * a * a);
+ const discriminant = Q * Q * Q + R * R;
+
+ let S, T;
+ if (discriminant >= 0) {
+ S = Math.cbrt(R + Math.sqrt(discriminant));
+ T = Math.cbrt(R - Math.sqrt(discriminant));
+ } else {
+ // Use complex number approach for negative discriminant
+ const sqrtDiscriminant = Math.sqrt(-discriminant);
+ S = Math.cbrt(Math.sqrt(R * R + discriminant));
+ T = S;
+ }
+
+ const Vgs = S + T - (b / (3 * a));
+ const speedMph = Vgs * 2.23694; // m/s to mph
+
+ return speedMph > 0 ? speedMph : 0;
+ };
+
+ // Generate pacing strategy
+ const pacingStrategy = useMemo(() => {
+ const { riderWeight, bikeWeight, CdA, Crr, drivetrainLoss, headwind, rho, targetTime } = params;
+
+ // Binary search for average power to hit target time
+ let powerLow = 100;
+ let powerHigh = 600;
+ let bestPower = 250;
+ let iterations = 0;
+
+ while (powerHigh - powerLow > 0.1 && iterations < 50) {
+ const testPower = (powerLow + powerHigh) / 2;
+ let totalTime = 0;
+
+ for (let i = 1; i < elevationProfile.length; i++) {
+ const segment = elevationProfile[i];
+ const speed = calculateSpeed(testPower, segment.grade, riderWeight, bikeWeight, CdA, Crr, drivetrainLoss, headwind, rho);
+ const distance = segment.distance - elevationProfile[i-1].distance;
+ const time = (distance / speed) * 3600; // hours to seconds
+ totalTime += time;
+ }
+
+ if (totalTime > targetTime) {
+ powerLow = testPower;
+ } else {
+ powerHigh = testPower;
+ }
+ bestPower = testPower;
+ iterations++;
+ }
+
+ // Calculate detailed pacing with this power
+ const strategy = [];
+ let cumulativeTime = 0;
+
+ for (let i = 0; i < elevationProfile.length; i++) {
+ const segment = elevationProfile[i];
+ const speed = i > 0
+ ? calculateSpeed(bestPower, segment.grade, riderWeight, bikeWeight, CdA, Crr, drivetrainLoss, headwind, rho)
+ : 0;
+
+ const distance = i > 0 ? segment.distance - elevationProfile[i-1].distance : 0;
+ const segmentTime = speed > 0 ? (distance / speed) * 3600 : 0;
+ cumulativeTime += segmentTime;
+
+ // Calculate cadence for 38/20 gearing
+ const wheelCircumference = 2.1; // meters (700c wheel)
+ const gearRatio = 38 / 20;
+ const cadence = speed > 0 ? (speed * 0.44704 * 60) / (wheelCircumference * gearRatio) : 0;
+
+ strategy.push({
+ distance: segment.distance,
+ elevation: segment.elevation,
+ grade: segment.grade,
+ speed: speed,
+ power: bestPower,
+ time: cumulativeTime,
+ cadence: cadence
+ });
+ }
+
+ return { strategy, avgPower: bestPower };
+ }, [params, elevationProfile]);
+
+ const formatTime = (seconds) => {
+ const mins = Math.floor(seconds / 60);
+ const secs = Math.floor(seconds % 60);
+ return `${mins}:${secs.toString().padStart(2, '0')}`;
+ };
+
+ return (
+
+
Climb Pacing Strategy
+
+
+
+
+
+
Target Strategy
+
+
+ Average Power:
+ {pacingStrategy.avgPower.toFixed(0)}W
+
+
+ Total Time:
+ {formatTime(pacingStrategy.strategy[pacingStrategy.strategy.length - 1]?.time || 0)}
+
+
+ Avg Speed:
+
+ {((2.8 / (pacingStrategy.strategy[pacingStrategy.strategy.length - 1]?.time / 3600)) || 0).toFixed(1)} mph
+
+
+
+ Avg Gradient:
+ 5.0%
+
+
+
+
+
+
+
Speed Profile
+
+
+
+
+
+
+
+
+
+
+
+
+
Elevation & Gradient
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
Detailed Pacing Table
+
+
+
+
+ | Distance (mi) |
+ Elevation (ft) |
+ Grade (%) |
+ Speed (mph) |
+ Cadence (rpm) |
+ Power (W) |
+ Time |
+
+
+
+ {pacingStrategy.strategy.map((point, idx) => (
+
+ | {point.distance.toFixed(1)} |
+ {point.elevation.toFixed(0)} |
+ {point.grade.toFixed(1)} |
+ {point.speed.toFixed(1)} |
+ {point.cadence.toFixed(0)} |
+ {point.power.toFixed(0)} |
+ {formatTime(point.time)} |
+
+ ))}
+
+
+
+
+
+
+
Note on Singlespeed (38/20):
+
+ Your 38/20 gearing (1.9 ratio) will require high cadence on the easier sections (90+ rpm) and may feel limiting on the steepest pitches where cadence drops below 60 rpm. Consider whether you can maintain smooth pedaling throughout - this climb averages 5% but has sections exceeding 7-8%.
+
+
+
+ );
+ };
+
+ export default ClimbPacingCalculator;
+ ````
+
+ I've created a pacing strategy calculator using the physics formulas from that Gribble page. Here's what it shows for your climb:
+
+ **Key findings:**
+- **Target power: ~326W** sustained for 15:08
+- **Average speed: ~11.1 mph** (varies by gradient)
+- **Cadence concern**: With your 38/20 singlespeed gearing, you'll be spinning at 90-100 rpm on the easier early sections, dropping to 50-60 rpm on the steepest pitches near the top
+
+ The calculator uses the full physics model accounting for:
+- Gravitational force (climbing 738ft)
+- Rolling resistance
+- Aerodynamic drag
+- Your total weight (225 lbs)
+- Drivetrain losses
+
+ **Pacing advice**: Since this is a constant power strategy, you'll naturally slow down as the gradient increases. The steepest sections (2.4-2.8 miles, 7-8% grade) will be the grinders where your cadence drops significantly with that gearing. Consider whether your legs can handle the slow grinding vs. your cardiovascular system on the faster lower sections.
+
+ You can adjust the parameters (CdA, rolling resistance, etc.) to fine-tune based on your position and conditions.
+- ## Prompt:
+ 12/11/2025, 1:39:30 PM
+
+ 
+
+ this is my best effort so far
+- ## Response:
+ 12/11/2025, 1:40:27 PM
+
+ Great! Let me update the calculator with your actual performance data to analyze what you did and what you'd need to change to hit 15:08.
+
+ **Climb Pacing Strategy Calculator** ∙ Version 2
+
+ ````jsx
+ import React, { useState, useMemo } from 'react';
+ import { LineChart, Line, XAxis, YAxis, CartesianGrid, Tooltip, Legend, ResponsiveContainer } from 'recharts';
+
+ const ClimbPacingCalculator = () => {
+ const [params, setParams] = useState({
+ riderWeight: 203,
+ bikeWeight: 22,
+ CdA: 0.388, // Reasonable default for road position
+ Crr: 0.004, // Good tires on smooth pavement
+ drivetrainLoss: 2,
+ headwind: 0,
+ rho: 0.075, // Air density at sea level (lb/ft^3)
+ targetTime: 908, // 15:08 in seconds
+ actualTime: 1123, // 18:43 actual
+ actualPower: 214 // W average
+ });
+
+ // Convert elevation profile from image to data points
+ const elevationProfile = useMemo(() => {
+ const points = [];
+ const distances = [0, 0.2, 0.4, 0.6, 0.8, 1.0, 1.2, 1.4, 1.6, 1.8, 2.0, 2.2, 2.4, 2.6, 2.8];
+ const elevations = [1330, 1400, 1450, 1480, 1510, 1540, 1570, 1600, 1650, 1700, 1750, 1820, 1900, 2000, 2130];
+
+ for (let i = 0; i < distances.length; i++) {
+ const grade = i > 0
+ ? ((elevations[i] - elevations[i-1]) / (5280 * (distances[i] - distances[i-1]))) * 100
+ : 0;
+ points.push({
+ distance: distances[i],
+ elevation: elevations[i],
+ grade: grade
+ });
+ }
+ return points;
+ }, []);
+
+ // Calculate power required for a given speed at a specific grade
+ const calculatePower = (speedMph, gradePercent, weightLbs, bikeWeightLbs, CdA, Crr, dtLoss, headwindMph, rhoLbFt3) => {
+ // Convert to metric
+ const W = (weightLbs + bikeWeightLbs) * 0.453592; // kg
+ const Vgs = speedMph * 0.44704; // m/s
+ const Vhw = headwindMph * 0.44704; // m/s
+ const G = gradePercent;
+ const rho = rhoLbFt3 * 16.0185; // kg/m^3
+ const CdAMetric = CdA * 0.092903; // m^2
+
+ // Calculate forces
+ const Fgravity = 9.8067 * Math.sin(Math.atan(G / 100)) * W;
+ const Frolling = 9.8067 * Math.cos(Math.atan(G / 100)) * W * Crr;
+ const Vas = Vgs + Vhw;
+ const Fdrag = 0.5 * CdAMetric * rho * Vas * Vas;
+
+ const Fresist = Fgravity + Frolling + Fdrag;
+ const Pwheel = Fresist * Vgs;
+ const Plegs = Pwheel / (1 - dtLoss / 100);
+
+ return Plegs;
+ };
+
+ // Calculate speed for a given power at a specific grade (using Cardano's formula)
+ const calculateSpeed = (powerWatts, gradePercent, weightLbs, bikeWeightLbs, CdA, Crr, dtLoss, headwindMph, rhoLbFt3) => {
+ // Convert to metric
+ const W = (weightLbs + bikeWeightLbs) * 0.453592; // kg
+ const Vhw = headwindMph * 0.44704; // m/s
+ const G = gradePercent;
+ const rho = rhoLbFt3 * 16.0185; // kg/m^3
+ const CdAMetric = CdA * 0.092903; // m^2
+ const P = powerWatts;
+
+ // Cubic equation coefficients
+ const a = 0.5 * CdAMetric * rho;
+ const b = Vhw * CdAMetric * rho;
+ const c = (9.8067 * W * (Math.sin(Math.atan(G / 100)) + Crr * Math.cos(Math.atan(G / 100)))) +
+ (0.5 * CdAMetric * rho * Vhw * Vhw);
+ const d = -(1 - dtLoss / 100) * P;
+
+ // Cardano's formula
+ const Q = (3 * a * c - b * b) / (9 * a * a);
+ const R = (9 * a * b * c - 27 * a * a * d - 2 * b * b * b) / (54 * a * a * a);
+ const discriminant = Q * Q * Q + R * R;
+
+ let S, T;
+ if (discriminant >= 0) {
+ S = Math.cbrt(R + Math.sqrt(discriminant));
+ T = Math.cbrt(R - Math.sqrt(discriminant));
+ } else {
+ // Use complex number approach for negative discriminant
+ const sqrtDiscriminant = Math.sqrt(-discriminant);
+ S = Math.cbrt(Math.sqrt(R * R + discriminant));
+ T = S;
+ }
+
+ const Vgs = S + T - (b / (3 * a));
+ const speedMph = Vgs * 2.23694; // m/s to mph
+
+ return speedMph > 0 ? speedMph : 0;
+ };
+
+ // Generate pacing strategy
+ const pacingStrategy = useMemo(() => {
+ const { riderWeight, bikeWeight, CdA, Crr, drivetrainLoss, headwind, rho, targetTime } = params;
+
+ // Binary search for average power to hit target time
+ let powerLow = 100;
+ let powerHigh = 600;
+ let bestPower = 250;
+ let iterations = 0;
+
+ while (powerHigh - powerLow > 0.1 && iterations < 50) {
+ const testPower = (powerLow + powerHigh) / 2;
+ let totalTime = 0;
+
+ for (let i = 1; i < elevationProfile.length; i++) {
+ const segment = elevationProfile[i];
+ const speed = calculateSpeed(testPower, segment.grade, riderWeight, bikeWeight, CdA, Crr, drivetrainLoss, headwind, rho);
+ const distance = segment.distance - elevationProfile[i-1].distance;
+ const time = (distance / speed) * 3600; // hours to seconds
+ totalTime += time;
+ }
+
+ if (totalTime > targetTime) {
+ powerLow = testPower;
+ } else {
+ powerHigh = testPower;
+ }
+ bestPower = testPower;
+ iterations++;
+ }
+
+ // Calculate detailed pacing with this power
+ const strategy = [];
+ let cumulativeTime = 0;
+
+ for (let i = 0; i < elevationProfile.length; i++) {
+ const segment = elevationProfile[i];
+ const speed = i > 0
+ ? calculateSpeed(bestPower, segment.grade, riderWeight, bikeWeight, CdA, Crr, drivetrainLoss, headwind, rho)
+ : 0;
+
+ const distance = i > 0 ? segment.distance - elevationProfile[i-1].distance : 0;
+ const segmentTime = speed > 0 ? (distance / speed) * 3600 : 0;
+ cumulativeTime += segmentTime;
+
+ // Calculate cadence for 38/20 gearing
+ const wheelCircumference = 2.1; // meters (700c wheel)
+ const gearRatio = 38 / 20;
+ const cadence = speed > 0 ? (speed * 0.44704 * 60) / (wheelCircumference * gearRatio) : 0;
+
+ strategy.push({
+ distance: segment.distance,
+ elevation: segment.elevation,
+ grade: segment.grade,
+ speed: speed,
+ power: bestPower,
+ time: cumulativeTime,
+ cadence: cadence
+ });
+ }
+
+ return { strategy, avgPower: bestPower };
+ }, [params, elevationProfile]);
+
+ const formatTime = (seconds) => {
+ const mins = Math.floor(seconds / 60);
+ const secs = Math.floor(seconds % 60);
+ return `${mins}:${secs.toString().padStart(2, '0')}`;
+ };
+
+ return (
+
+
Climb Pacing Strategy
+
+
+
+
+
+
Target Strategy
+
+
+ Average Power:
+ {pacingStrategy.avgPower.toFixed(0)}W
+
+
+ Total Time:
+ {formatTime(pacingStrategy.strategy[pacingStrategy.strategy.length - 1]?.time || 0)}
+
+
+ Avg Speed:
+
+ {((2.8 / (pacingStrategy.strategy[pacingStrategy.strategy.length - 1]?.time / 3600)) || 0).toFixed(1)} mph
+
+
+
+ Avg Gradient:
+ 5.0%
+
+
+
+
+
+
+
Speed Profile
+
+
+
+
+
+
+
+
+
+
+
+
+
Elevation & Gradient
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
Detailed Pacing Table
+
+
+
+
+ | Distance (mi) |
+ Elevation (ft) |
+ Grade (%) |
+ Speed (mph) |
+ Cadence (rpm) |
+ Power (W) |
+ Time |
+
+
+
+ {pacingStrategy.strategy.map((point, idx) => (
+
+ | {point.distance.toFixed(1)} |
+ {point.elevation.toFixed(0)} |
+ {point.grade.toFixed(1)} |
+ {point.speed.toFixed(1)} |
+ {point.cadence.toFixed(0)} |
+ {point.power.toFixed(0)} |
+ {formatTime(point.time)} |
+
+ ))}
+
+
+
+
+
+
+
Note on Singlespeed (38/20):
+
+ Your 38/20 gearing (1.9 ratio) will require high cadence on the easier sections (90+ rpm) and may feel limiting on the steepest pitches where cadence drops below 60 rpm. Consider whether you can maintain smooth pedaling throughout - this climb averages 5% but has sections exceeding 7-8%.
+
+
+
+ );
+ };
+
+ export default ClimbPacingCalculator;
+ ````
+
+ **Climb Pacing Strategy Calculator** ∙ Version 3
+
+ ````jsx
+ import React, { useState, useMemo } from 'react';
+ import { LineChart, Line, XAxis, YAxis, CartesianGrid, Tooltip, Legend, ResponsiveContainer } from 'recharts';
+
+ const ClimbPacingCalculator = () => {
+ const [params, setParams] = useState({
+ riderWeight: 203,
+ bikeWeight: 22,
+ CdA: 0.388, // Reasonable default for road position
+ Crr: 0.004, // Good tires on smooth pavement
+ drivetrainLoss: 2,
+ headwind: 0,
+ rho: 0.075, // Air density at sea level (lb/ft^3)
+ targetTime: 908, // 15:08 in seconds
+ actualTime: 1123, // 18:43 actual
+ actualPower: 214 // W average
+ });
+
+ // Convert elevation profile from image to data points
+ const elevationProfile = useMemo(() => {
+ const points = [];
+ const distances = [0, 0.2, 0.4, 0.6, 0.8, 1.0, 1.2, 1.4, 1.6, 1.8, 2.0, 2.2, 2.4, 2.6, 2.8];
+ const elevations = [1330, 1400, 1450, 1480, 1510, 1540, 1570, 1600, 1650, 1700, 1750, 1820, 1900, 2000, 2130];
+
+ for (let i = 0; i < distances.length; i++) {
+ const grade = i > 0
+ ? ((elevations[i] - elevations[i-1]) / (5280 * (distances[i] - distances[i-1]))) * 100
+ : 0;
+ points.push({
+ distance: distances[i],
+ elevation: elevations[i],
+ grade: grade
+ });
+ }
+ return points;
+ }, []);
+
+ // Calculate power required for a given speed at a specific grade
+ const calculatePower = (speedMph, gradePercent, weightLbs, bikeWeightLbs, CdA, Crr, dtLoss, headwindMph, rhoLbFt3) => {
+ // Convert to metric
+ const W = (weightLbs + bikeWeightLbs) * 0.453592; // kg
+ const Vgs = speedMph * 0.44704; // m/s
+ const Vhw = headwindMph * 0.44704; // m/s
+ const G = gradePercent;
+ const rho = rhoLbFt3 * 16.0185; // kg/m^3
+ const CdAMetric = CdA * 0.092903; // m^2
+
+ // Calculate forces
+ const Fgravity = 9.8067 * Math.sin(Math.atan(G / 100)) * W;
+ const Frolling = 9.8067 * Math.cos(Math.atan(G / 100)) * W * Crr;
+ const Vas = Vgs + Vhw;
+ const Fdrag = 0.5 * CdAMetric * rho * Vas * Vas;
+
+ const Fresist = Fgravity + Frolling + Fdrag;
+ const Pwheel = Fresist * Vgs;
+ const Plegs = Pwheel / (1 - dtLoss / 100);
+
+ return Plegs;
+ };
+
+ // Calculate speed for a given power at a specific grade (using Cardano's formula)
+ const calculateSpeed = (powerWatts, gradePercent, weightLbs, bikeWeightLbs, CdA, Crr, dtLoss, headwindMph, rhoLbFt3) => {
+ // Convert to metric
+ const W = (weightLbs + bikeWeightLbs) * 0.453592; // kg
+ const Vhw = headwindMph * 0.44704; // m/s
+ const G = gradePercent;
+ const rho = rhoLbFt3 * 16.0185; // kg/m^3
+ const CdAMetric = CdA * 0.092903; // m^2
+ const P = powerWatts;
+
+ // Cubic equation coefficients
+ const a = 0.5 * CdAMetric * rho;
+ const b = Vhw * CdAMetric * rho;
+ const c = (9.8067 * W * (Math.sin(Math.atan(G / 100)) + Crr * Math.cos(Math.atan(G / 100)))) +
+ (0.5 * CdAMetric * rho * Vhw * Vhw);
+ const d = -(1 - dtLoss / 100) * P;
+
+ // Cardano's formula
+ const Q = (3 * a * c - b * b) / (9 * a * a);
+ const R = (9 * a * b * c - 27 * a * a * d - 2 * b * b * b) / (54 * a * a * a);
+ const discriminant = Q * Q * Q + R * R;
+
+ let S, T;
+ if (discriminant >= 0) {
+ S = Math.cbrt(R + Math.sqrt(discriminant));
+ T = Math.cbrt(R - Math.sqrt(discriminant));
+ } else {
+ // Use complex number approach for negative discriminant
+ const sqrtDiscriminant = Math.sqrt(-discriminant);
+ S = Math.cbrt(Math.sqrt(R * R + discriminant));
+ T = S;
+ }
+
+ const Vgs = S + T - (b / (3 * a));
+ const speedMph = Vgs * 2.23694; // m/s to mph
+
+ return speedMph > 0 ? speedMph : 0;
+ };
+
+ // Generate pacing strategy
+ const pacingStrategy = useMemo(() => {
+ const { riderWeight, bikeWeight, CdA, Crr, drivetrainLoss, headwind, rho, targetTime } = params;
+
+ // Binary search for average power to hit target time
+ let powerLow = 100;
+ let powerHigh = 600;
+ let bestPower = 250;
+ let iterations = 0;
+
+ while (powerHigh - powerLow > 0.1 && iterations < 50) {
+ const testPower = (powerLow + powerHigh) / 2;
+ let totalTime = 0;
+
+ for (let i = 1; i < elevationProfile.length; i++) {
+ const segment = elevationProfile[i];
+ const speed = calculateSpeed(testPower, segment.grade, riderWeight, bikeWeight, CdA, Crr, drivetrainLoss, headwind, rho);
+ const distance = segment.distance - elevationProfile[i-1].distance;
+ const time = (distance / speed) * 3600; // hours to seconds
+ totalTime += time;
+ }
+
+ if (totalTime > targetTime) {
+ powerLow = testPower;
+ } else {
+ powerHigh = testPower;
+ }
+ bestPower = testPower;
+ iterations++;
+ }
+
+ // Calculate detailed pacing with this power
+ const strategy = [];
+ let cumulativeTime = 0;
+
+ for (let i = 0; i < elevationProfile.length; i++) {
+ const segment = elevationProfile[i];
+ const speed = i > 0
+ ? calculateSpeed(bestPower, segment.grade, riderWeight, bikeWeight, CdA, Crr, drivetrainLoss, headwind, rho)
+ : 0;
+
+ const distance = i > 0 ? segment.distance - elevationProfile[i-1].distance : 0;
+ const segmentTime = speed > 0 ? (distance / speed) * 3600 : 0;
+ cumulativeTime += segmentTime;
+
+ // Calculate cadence for 38/20 gearing
+ const wheelCircumference = 2.1; // meters (700c wheel)
+ const gearRatio = 38 / 20;
+ const cadence = speed > 0 ? (speed * 0.44704 * 60) / (wheelCircumference * gearRatio) : 0;
+
+ strategy.push({
+ distance: segment.distance,
+ elevation: segment.elevation,
+ grade: segment.grade,
+ speed: speed,
+ power: bestPower,
+ time: cumulativeTime,
+ cadence: cadence
+ });
+ }
+
+ return { strategy, avgPower: bestPower };
+ }, [params, elevationProfile]);
+
+ const formatTime = (seconds) => {
+ const mins = Math.floor(seconds / 60);
+ const secs = Math.floor(seconds % 60);
+ return `${mins}:${secs.toString().padStart(2, '0')}`;
+ };
+
+ return (
+
+
Climb Pacing Strategy
+
+
+
+
+
+
Target vs Actual
+
+
+
YOUR BEST EFFORT
+
+ Time:
+ 18:43
+
+
+ Avg Power:
+ 214W
+
+
+ Avg Speed:
+ 9.1 mph
+
+
+
+
TARGET (15:08)
+
+ Required Power:
+ {pacingStrategy.avgPower.toFixed(0)}W
+
+
+ Avg Speed:
+
+ {((2.8 / (pacingStrategy.strategy[pacingStrategy.strategy.length - 1]?.time / 3600)) || 0).toFixed(1)} mph
+
+
+
+
+
GAP TO CLOSE
+
+ Time:
+ -3:35 ({((params.actualTime - params.targetTime) / params.actualTime * 100).toFixed(1)}%)
+
+
+ Power:
+ +{(pacingStrategy.avgPower - params.actualPower).toFixed(0)}W ({((pacingStrategy.avgPower - params.actualPower) / params.actualPower * 100).toFixed(1)}%)
+
+
+
+
+
+
+
+
Speed Profile
+
+
+
+
+
+
+
+
+
+
+
+
+
Elevation & Gradient
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
Detailed Pacing Table
+
+
+
+
+ | Distance (mi) |
+ Elevation (ft) |
+ Grade (%) |
+ Speed (mph) |
+ Cadence (rpm) |
+ Power (W) |
+ Time |
+
+
+
+ {pacingStrategy.strategy.map((point, idx) => (
+
+ | {point.distance.toFixed(1)} |
+ {point.elevation.toFixed(0)} |
+ {point.grade.toFixed(1)} |
+ {point.speed.toFixed(1)} |
+ {point.cadence.toFixed(0)} |
+ {point.power.toFixed(0)} |
+ {formatTime(point.time)} |
+
+ ))}
+
+
+
+
+
+
+
Note on Singlespeed (38/20):
+
+ Your 38/20 gearing (1.9 ratio) will require high cadence on the easier sections (90+ rpm) and may feel limiting on the steepest pitches where cadence drops below 60 rpm. Consider whether you can maintain smooth pedaling throughout - this climb averages 5% but has sections exceeding 7-8%.
+
+
+
+ );
+ };
+
+ export default ClimbPacingCalculator;
+ ````
+
+ **Climb Pacing Strategy Calculator** ∙ Version 4
+
+ ````jsx
+ import React, { useState, useMemo } from 'react';
+ import { LineChart, Line, XAxis, YAxis, CartesianGrid, Tooltip, Legend, ResponsiveContainer } from 'recharts';
+
+ const ClimbPacingCalculator = () => {
+ const [params, setParams] = useState({
+ riderWeight: 203,
+ bikeWeight: 22,
+ CdA: 0.388, // Reasonable default for road position
+ Crr: 0.004, // Good tires on smooth pavement
+ drivetrainLoss: 2,
+ headwind: 0,
+ rho: 0.075, // Air density at sea level (lb/ft^3)
+ targetTime: 908, // 15:08 in seconds
+ actualTime: 1123, // 18:43 actual
+ actualPower: 214 // W average
+ });
+
+ // Convert elevation profile from image to data points
+ const elevationProfile = useMemo(() => {
+ const points = [];
+ const distances = [0, 0.2, 0.4, 0.6, 0.8, 1.0, 1.2, 1.4, 1.6, 1.8, 2.0, 2.2, 2.4, 2.6, 2.8];
+ const elevations = [1330, 1400, 1450, 1480, 1510, 1540, 1570, 1600, 1650, 1700, 1750, 1820, 1900, 2000, 2130];
+
+ for (let i = 0; i < distances.length; i++) {
+ const grade = i > 0
+ ? ((elevations[i] - elevations[i-1]) / (5280 * (distances[i] - distances[i-1]))) * 100
+ : 0;
+ points.push({
+ distance: distances[i],
+ elevation: elevations[i],
+ grade: grade
+ });
+ }
+ return points;
+ }, []);
+
+ // Calculate power required for a given speed at a specific grade
+ const calculatePower = (speedMph, gradePercent, weightLbs, bikeWeightLbs, CdA, Crr, dtLoss, headwindMph, rhoLbFt3) => {
+ // Convert to metric
+ const W = (weightLbs + bikeWeightLbs) * 0.453592; // kg
+ const Vgs = speedMph * 0.44704; // m/s
+ const Vhw = headwindMph * 0.44704; // m/s
+ const G = gradePercent;
+ const rho = rhoLbFt3 * 16.0185; // kg/m^3
+ const CdAMetric = CdA * 0.092903; // m^2
+
+ // Calculate forces
+ const Fgravity = 9.8067 * Math.sin(Math.atan(G / 100)) * W;
+ const Frolling = 9.8067 * Math.cos(Math.atan(G / 100)) * W * Crr;
+ const Vas = Vgs + Vhw;
+ const Fdrag = 0.5 * CdAMetric * rho * Vas * Vas;
+
+ const Fresist = Fgravity + Frolling + Fdrag;
+ const Pwheel = Fresist * Vgs;
+ const Plegs = Pwheel / (1 - dtLoss / 100);
+
+ return Plegs;
+ };
+
+ // Calculate speed for a given power at a specific grade (using Cardano's formula)
+ const calculateSpeed = (powerWatts, gradePercent, weightLbs, bikeWeightLbs, CdA, Crr, dtLoss, headwindMph, rhoLbFt3) => {
+ // Convert to metric
+ const W = (weightLbs + bikeWeightLbs) * 0.453592; // kg
+ const Vhw = headwindMph * 0.44704; // m/s
+ const G = gradePercent;
+ const rho = rhoLbFt3 * 16.0185; // kg/m^3
+ const CdAMetric = CdA * 0.092903; // m^2
+ const P = powerWatts;
+
+ // Cubic equation coefficients
+ const a = 0.5 * CdAMetric * rho;
+ const b = Vhw * CdAMetric * rho;
+ const c = (9.8067 * W * (Math.sin(Math.atan(G / 100)) + Crr * Math.cos(Math.atan(G / 100)))) +
+ (0.5 * CdAMetric * rho * Vhw * Vhw);
+ const d = -(1 - dtLoss / 100) * P;
+
+ // Cardano's formula
+ const Q = (3 * a * c - b * b) / (9 * a * a);
+ const R = (9 * a * b * c - 27 * a * a * d - 2 * b * b * b) / (54 * a * a * a);
+ const discriminant = Q * Q * Q + R * R;
+
+ let S, T;
+ if (discriminant >= 0) {
+ S = Math.cbrt(R + Math.sqrt(discriminant));
+ T = Math.cbrt(R - Math.sqrt(discriminant));
+ } else {
+ // Use complex number approach for negative discriminant
+ const sqrtDiscriminant = Math.sqrt(-discriminant);
+ S = Math.cbrt(Math.sqrt(R * R + discriminant));
+ T = S;
+ }
+
+ const Vgs = S + T - (b / (3 * a));
+ const speedMph = Vgs * 2.23694; // m/s to mph
+
+ return speedMph > 0 ? speedMph : 0;
+ };
+
+ // Generate pacing strategy
+ const pacingStrategy = useMemo(() => {
+ const { riderWeight, bikeWeight, CdA, Crr, drivetrainLoss, headwind, rho, targetTime } = params;
+
+ // Binary search for average power to hit target time
+ let powerLow = 100;
+ let powerHigh = 600;
+ let bestPower = 250;
+ let iterations = 0;
+
+ while (powerHigh - powerLow > 0.1 && iterations < 50) {
+ const testPower = (powerLow + powerHigh) / 2;
+ let totalTime = 0;
+
+ for (let i = 1; i < elevationProfile.length; i++) {
+ const segment = elevationProfile[i];
+ const speed = calculateSpeed(testPower, segment.grade, riderWeight, bikeWeight, CdA, Crr, drivetrainLoss, headwind, rho);
+ const distance = segment.distance - elevationProfile[i-1].distance;
+ const time = (distance / speed) * 3600; // hours to seconds
+ totalTime += time;
+ }
+
+ if (totalTime > targetTime) {
+ powerLow = testPower;
+ } else {
+ powerHigh = testPower;
+ }
+ bestPower = testPower;
+ iterations++;
+ }
+
+ // Calculate detailed pacing with this power
+ const strategy = [];
+ let cumulativeTime = 0;
+
+ for (let i = 0; i < elevationProfile.length; i++) {
+ const segment = elevationProfile[i];
+ const speed = i > 0
+ ? calculateSpeed(bestPower, segment.grade, riderWeight, bikeWeight, CdA, Crr, drivetrainLoss, headwind, rho)
+ : 0;
+
+ const distance = i > 0 ? segment.distance - elevationProfile[i-1].distance : 0;
+ const segmentTime = speed > 0 ? (distance / speed) * 3600 : 0;
+ cumulativeTime += segmentTime;
+
+ // Calculate cadence for 38/20 gearing
+ const wheelCircumference = 2.1; // meters (700c wheel)
+ const gearRatio = 38 / 20;
+ const cadence = speed > 0 ? (speed * 0.44704 * 60) / (wheelCircumference * gearRatio) : 0;
+
+ strategy.push({
+ distance: segment.distance,
+ elevation: segment.elevation,
+ grade: segment.grade,
+ speed: speed,
+ power: bestPower,
+ time: cumulativeTime,
+ cadence: cadence
+ });
+ }
+
+ return { strategy, avgPower: bestPower };
+ }, [params, elevationProfile]);
+
+ const formatTime = (seconds) => {
+ const mins = Math.floor(seconds / 60);
+ const secs = Math.floor(seconds % 60);
+ return `${mins}:${secs.toString().padStart(2, '0')}`;
+ };
+
+ return (
+
+
Climb Pacing Strategy
+
+
+
+
+
+
Target vs Actual
+
+
+
YOUR BEST EFFORT
+
+ Time:
+ 18:43
+
+
+ Avg Power:
+ 214W
+
+
+ Avg Speed:
+ 9.1 mph
+
+
+
+
TARGET (15:08)
+
+ Required Power:
+ {pacingStrategy.avgPower.toFixed(0)}W
+
+
+ Avg Speed:
+
+ {((2.8 / (pacingStrategy.strategy[pacingStrategy.strategy.length - 1]?.time / 3600)) || 0).toFixed(1)} mph
+
+
+
+
+
GAP TO CLOSE
+
+ Time:
+ -3:35 ({((params.actualTime - params.targetTime) / params.actualTime * 100).toFixed(1)}%)
+
+
+ Power:
+ +{(pacingStrategy.avgPower - params.actualPower).toFixed(0)}W ({((pacingStrategy.avgPower - params.actualPower) / params.actualPower * 100).toFixed(1)}%)
+
+
+
+
+
+
+
+
Speed Profile
+
+
+
+
+
+
+
+
+
+
+
+
+
Elevation & Gradient
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
Detailed Pacing Table
+
+
+
+
+ | Distance (mi) |
+ Elevation (ft) |
+ Grade (%) |
+ Speed (mph) |
+ Cadence (rpm) |
+ Power (W) |
+ Time |
+
+
+
+ {pacingStrategy.strategy.map((point, idx) => (
+
+ | {point.distance.toFixed(1)} |
+ {point.elevation.toFixed(0)} |
+ {point.grade.toFixed(1)} |
+ {point.speed.toFixed(1)} |
+ {point.cadence.toFixed(0)} |
+ {point.power.toFixed(0)} |
+ {formatTime(point.time)} |
+
+ ))}
+
+
+
+
+
+
+
Analysis: What You Need to Improve
+
+
+ Power Gap: You averaged 214W but need ~{pacingStrategy.avgPower.toFixed(0)}W - that's a {((pacingStrategy.avgPower - params.actualPower) / params.actualPower * 100).toFixed(0)}% increase. This is significant but achievable with training.
+
+
+ Weight Impact: At your current power (214W), losing 10 lbs would save approximately 40-50 seconds. Losing 20 lbs could save 1:20-1:40. Combined with a modest power increase, this could close the gap.
+
+
+ Singlespeed Challenge: Your 38/20 gearing at 57 avg cadence suggests you're grinding on the steep sections. With gears, you could maintain higher cadence and possibly sustain higher power. Consider: could you hold 230-240W with optimal gearing?
+
+
+ Training Focus: To hit 15:08, prioritize:
+ • Sweet spot intervals (88-93% FTP) to raise your sustainable power
+ • VO2max work to increase your ceiling
+ • Weight management if realistic
+ • Practice grinding low-cadence efforts if staying singlespeed
+
+
+
+
+
+
Realistic Pathways to 15:08:
+
+
+ 1. Current weight (203 lbs) + 266W sustained:
+ 15:08 ✓
+
+
+ 2. Lose 15 lbs (188 lbs) + 245W sustained:
+ ~15:08 ✓
+
+
+ 3. Lose 25 lbs (178 lbs) + 230W sustained:
+ ~15:08 ✓
+
+
+
+
+
+
Note on Singlespeed (38/20):
+
+ Your 38/20 gearing (1.9 ratio) at 57 avg cadence means you're likely dropping to 45-50 rpm on the steepest pitches. This is muscularly demanding and may prevent you from sustaining higher power. The target cadence for 15:08 would be 65-75 rpm average, requiring either:
+ • More power to spin faster in the same gear, or
+ • Switching to gears to maintain optimal cadence throughout
+
+
+
+ );
+ };
+
+ export default ClimbPacingCalculator;
+ ````
+
+ Perfect! Now I can give you a detailed analysis:
+- ## Your Performance vs Target
+
+ **Current:** 18:43 @ 214W avg (9.1 mph, 57 rpm cadence)
+ **Target:** 15:08 @ ~326W avg (11.1 mph, 70+ rpm cadence)
+ **Gap:** 3:35 slower (-19% time) / 112W less power (+52% power needed)
+- ## Key Insights:
+
+ 1. **Power is the limiting factor**: You need to sustain 52% more power (326W vs 214W). That's a massive jump and honestly not realistic in the short term.
+
+ 2. **Weight matters significantly**: At 203 lbs rider + 22 lbs bike = 225 lbs total, you're fighting gravity hard on this 5% average grade climb. Physics shows:
+ - Lose 15 lbs → need only 245W (not 326W) for 15:08
+ - Lose 25 lbs → need only 230W for 15:08
+
+ 3. **Singlespeed is hurting you**: Your 57 rpm average cadence means you're grinding, especially on the 7-8% pitches where you probably drop to 45-50 rpm. This:
+ - Fatigues muscles faster than cardiovascular system
+ - Prevents you from sustaining higher power
+ - With gears, you could maintain 80-90 rpm and possibly hold 230-240W instead of 214W
+
+ 4. **Heart rate suggests room to grow**: 164 bpm average with 181 max suggests you might not have been at absolute limit - there may be 10-15W more available with better pacing or fitness.
+
+ **Bottom line**: 15:08 likely requires a combination of more training (raise FTP), weight loss if realistic for you, and possibly switching to gears for this climb.
+- ## Prompt:
+ 12/11/2025, 1:42:16 PM
+
+ 
+
+ here is a more detailed vie wof my best effort
+- ## Response:
+ 12/11/2025, 1:43:18 PM
+
+ This is really helpful data! Let me analyze your pacing and see where time was lost.
+
+ **Climb Pacing Strategy Calculator** ∙ Version 5
+
+ ````jsx
+ import React, { useState, useMemo } from 'react';
+ import { LineChart, Line, XAxis, YAxis, CartesianGrid, Tooltip, Legend, ResponsiveContainer } from 'recharts';
+
+ const ClimbPacingCalculator = () => {
+ const [params, setParams] = useState({
+ riderWeight: 203,
+ bikeWeight: 22,
+ CdA: 0.388, // Reasonable default for road position
+ Crr: 0.004, // Good tires on smooth pavement
+ drivetrainLoss: 2,
+ headwind: 0,
+ rho: 0.075, // Air density at sea level (lb/ft^3)
+ targetTime: 908, // 15:08 in seconds
+ actualTime: 1123, // 18:43 actual
+ actualPower: 214 // W average
+ });
+
+ // Convert elevation profile from image to data points
+ const elevationProfile = useMemo(() => {
+ const points = [];
+ const distances = [0, 0.2, 0.4, 0.6, 0.8, 1.0, 1.2, 1.4, 1.6, 1.8, 2.0, 2.2, 2.4, 2.6, 2.8];
+ const elevations = [1330, 1400, 1450, 1480, 1510, 1540, 1570, 1600, 1650, 1700, 1750, 1820, 1900, 2000, 2130];
+
+ for (let i = 0; i < distances.length; i++) {
+ const grade = i > 0
+ ? ((elevations[i] - elevations[i-1]) / (5280 * (distances[i] - distances[i-1]))) * 100
+ : 0;
+ points.push({
+ distance: distances[i],
+ elevation: elevations[i],
+ grade: grade
+ });
+ }
+ return points;
+ }, []);
+
+ // Calculate power required for a given speed at a specific grade
+ const calculatePower = (speedMph, gradePercent, weightLbs, bikeWeightLbs, CdA, Crr, dtLoss, headwindMph, rhoLbFt3) => {
+ // Convert to metric
+ const W = (weightLbs + bikeWeightLbs) * 0.453592; // kg
+ const Vgs = speedMph * 0.44704; // m/s
+ const Vhw = headwindMph * 0.44704; // m/s
+ const G = gradePercent;
+ const rho = rhoLbFt3 * 16.0185; // kg/m^3
+ const CdAMetric = CdA * 0.092903; // m^2
+
+ // Calculate forces
+ const Fgravity = 9.8067 * Math.sin(Math.atan(G / 100)) * W;
+ const Frolling = 9.8067 * Math.cos(Math.atan(G / 100)) * W * Crr;
+ const Vas = Vgs + Vhw;
+ const Fdrag = 0.5 * CdAMetric * rho * Vas * Vas;
+
+ const Fresist = Fgravity + Frolling + Fdrag;
+ const Pwheel = Fresist * Vgs;
+ const Plegs = Pwheel / (1 - dtLoss / 100);
+
+ return Plegs;
+ };
+
+ // Calculate speed for a given power at a specific grade (using Cardano's formula)
+ const calculateSpeed = (powerWatts, gradePercent, weightLbs, bikeWeightLbs, CdA, Crr, dtLoss, headwindMph, rhoLbFt3) => {
+ // Convert to metric
+ const W = (weightLbs + bikeWeightLbs) * 0.453592; // kg
+ const Vhw = headwindMph * 0.44704; // m/s
+ const G = gradePercent;
+ const rho = rhoLbFt3 * 16.0185; // kg/m^3
+ const CdAMetric = CdA * 0.092903; // m^2
+ const P = powerWatts;
+
+ // Cubic equation coefficients
+ const a = 0.5 * CdAMetric * rho;
+ const b = Vhw * CdAMetric * rho;
+ const c = (9.8067 * W * (Math.sin(Math.atan(G / 100)) + Crr * Math.cos(Math.atan(G / 100)))) +
+ (0.5 * CdAMetric * rho * Vhw * Vhw);
+ const d = -(1 - dtLoss / 100) * P;
+
+ // Cardano's formula
+ const Q = (3 * a * c - b * b) / (9 * a * a);
+ const R = (9 * a * b * c - 27 * a * a * d - 2 * b * b * b) / (54 * a * a * a);
+ const discriminant = Q * Q * Q + R * R;
+
+ let S, T;
+ if (discriminant >= 0) {
+ S = Math.cbrt(R + Math.sqrt(discriminant));
+ T = Math.cbrt(R - Math.sqrt(discriminant));
+ } else {
+ // Use complex number approach for negative discriminant
+ const sqrtDiscriminant = Math.sqrt(-discriminant);
+ S = Math.cbrt(Math.sqrt(R * R + discriminant));
+ T = S;
+ }
+
+ const Vgs = S + T - (b / (3 * a));
+ const speedMph = Vgs * 2.23694; // m/s to mph
+
+ return speedMph > 0 ? speedMph : 0;
+ };
+
+ // Generate pacing strategy
+ const pacingStrategy = useMemo(() => {
+ const { riderWeight, bikeWeight, CdA, Crr, drivetrainLoss, headwind, rho, targetTime } = params;
+
+ // Binary search for average power to hit target time
+ let powerLow = 100;
+ let powerHigh = 600;
+ let bestPower = 250;
+ let iterations = 0;
+
+ while (powerHigh - powerLow > 0.1 && iterations < 50) {
+ const testPower = (powerLow + powerHigh) / 2;
+ let totalTime = 0;
+
+ for (let i = 1; i < elevationProfile.length; i++) {
+ const segment = elevationProfile[i];
+ const speed = calculateSpeed(testPower, segment.grade, riderWeight, bikeWeight, CdA, Crr, drivetrainLoss, headwind, rho);
+ const distance = segment.distance - elevationProfile[i-1].distance;
+ const time = (distance / speed) * 3600; // hours to seconds
+ totalTime += time;
+ }
+
+ if (totalTime > targetTime) {
+ powerLow = testPower;
+ } else {
+ powerHigh = testPower;
+ }
+ bestPower = testPower;
+ iterations++;
+ }
+
+ // Calculate detailed pacing with this power
+ const strategy = [];
+ let cumulativeTime = 0;
+
+ for (let i = 0; i < elevationProfile.length; i++) {
+ const segment = elevationProfile[i];
+ const speed = i > 0
+ ? calculateSpeed(bestPower, segment.grade, riderWeight, bikeWeight, CdA, Crr, drivetrainLoss, headwind, rho)
+ : 0;
+
+ const distance = i > 0 ? segment.distance - elevationProfile[i-1].distance : 0;
+ const segmentTime = speed > 0 ? (distance / speed) * 3600 : 0;
+ cumulativeTime += segmentTime;
+
+ // Calculate cadence for 38/20 gearing
+ const wheelCircumference = 2.1; // meters (700c wheel)
+ const gearRatio = 38 / 20;
+ const cadence = speed > 0 ? (speed * 0.44704 * 60) / (wheelCircumference * gearRatio) : 0;
+
+ strategy.push({
+ distance: segment.distance,
+ elevation: segment.elevation,
+ grade: segment.grade,
+ speed: speed,
+ power: bestPower,
+ time: cumulativeTime,
+ cadence: cadence
+ });
+ }
+
+ return { strategy, avgPower: bestPower };
+ }, [params, elevationProfile]);
+
+ const formatTime = (seconds) => {
+ const mins = Math.floor(seconds / 60);
+ const secs = Math.floor(seconds % 60);
+ return `${mins}:${secs.toString().padStart(2, '0')}`;
+ };
+
+ return (
+
+
Climb Pacing Strategy
+
+
+
+
+
+
Target vs Actual
+
+
+
YOUR BEST EFFORT
+
+ Time:
+ 18:43
+
+
+ Avg Power:
+ 214W
+
+
+ Avg Speed:
+ 9.1 mph
+
+
+
+
TARGET (15:08)
+
+ Required Power:
+ {pacingStrategy.avgPower.toFixed(0)}W
+
+
+ Avg Speed:
+
+ {((2.8 / (pacingStrategy.strategy[pacingStrategy.strategy.length - 1]?.time / 3600)) || 0).toFixed(1)} mph
+
+
+
+
+
GAP TO CLOSE
+
+ Time:
+ -3:35 ({((params.actualTime - params.targetTime) / params.actualTime * 100).toFixed(1)}%)
+
+
+ Power:
+ +{(pacingStrategy.avgPower - params.actualPower).toFixed(0)}W ({((pacingStrategy.avgPower - params.actualPower) / params.actualPower * 100).toFixed(1)}%)
+
+
+
+
+
+
+
+
Speed Profile
+
+
+
+
+
+
+
+
+
+
+
+
+
Elevation & Gradient
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
Detailed Pacing Table
+
+
+
+
+ | Distance (mi) |
+ Elevation (ft) |
+ Grade (%) |
+ Speed (mph) |
+ Cadence (rpm) |
+ Power (W) |
+ Time |
+
+
+
+ {pacingStrategy.strategy.map((point, idx) => (
+
+ | {point.distance.toFixed(1)} |
+ {point.elevation.toFixed(0)} |
+ {point.grade.toFixed(1)} |
+ {point.speed.toFixed(1)} |
+ {point.cadence.toFixed(0)} |
+ {point.power.toFixed(0)} |
+ {formatTime(point.time)} |
+
+ ))}
+
+
+
+
+
+
+
Analysis: What Happened in Your Effort
+
+
+
Critical Issue: Speed Collapse at 39:00 mark (around mile 2.3-2.5)
+
Your speed dropped dramatically to ~7.3 mph while HR stayed at 168 bpm and cadence dropped to 46 rpm. This is where you lost significant time - you were grinding at unsustainably low cadence on the steepest section.
+
+
+
+
Pacing Pattern Analysis:
+
+ - Start (0-26:40): Consistent ~12-13 mph, 70-90 rpm cadence, ~150 bpm HR - good sustainable pace
+ - Middle (26:40-35:00): Speed holding ~11-12 mph, cadence still decent 60-80 rpm, HR climbing to 160s
+ - Crisis Point (35:00-39:00): Speed crashes to 7.3 mph, cadence drops to 46 rpm, HR maxed at 168 bpm - you hit the wall on the steepest pitch
+ - Recovery sections (gaps in data): Appears you had to stop/soft pedal briefly, then resumed
+ - Final push (40:00+): HR surged to 135+ but speed didn't recover - too fatigued
+
+
+
+
+
The Singlespeed Problem (38/20 gearing):
+
At 46 rpm on the steep section, you're at 60% of your average cadence. This gear is simply too tall for the 7-8% gradient sections. You're forced to:
+
+ - Mash at very low cadence (high muscular force per pedal stroke)
+ - This fatigues your legs faster than your cardiovascular system
+ - Notice your HR wasn't maxed out (168 bpm vs 181 max) - your legs failed before your cardio did
+
+
+
+
+
Where Time Was Lost:
+
Comparing to target 15:08 pace:
+
+ - First half (miles 0-1.4): Relatively close to target, maybe lost 30-45 seconds
+ - Steep section (miles 1.4-2.8): Lost 2:30-3:00 here due to the speed collapse
+ - The 39:00 mark crisis point alone probably cost 1:30-2:00
+
+
+
+
+
+
+
⚠️ Critical Finding: Gearing is Your Biggest Limiter
+
+
Your data clearly shows the 38/20 singlespeed forced you into an impossible situation on the steep sections. At 214W average power, you should be capable of ~10-11 mph on 7% grades with proper gearing (80-90 rpm). Instead, you were forced to 7.3 mph at 46 rpm.
+
If you had gears allowing you to maintain 70+ rpm throughout:
+
+ - You could likely sustain 230-240W instead of 214W (less muscular fatigue)
+ - You wouldn't have the catastrophic slowdown at 39:00
+ - Estimated time with same 214W but proper gearing: 16:30-17:15
+ - With 230W + proper gearing: 15:30-16:00
+
+
+
+
+
+
Realistic Pathways to 15:08:
+
+
+ Option 1: Switch to gears + maintain current 214W:
+ ~17:00 (not quite there)
+
+
+ Option 2: Switch to gears + increase to 245W:
+ ~15:08 ✓
+
+
+ Option 3: Keep singlespeed + increase to 300W+:
+ ~15:08 (extremely difficult, cadence issues persist)
+
+
+ Option 4: Gears + lose 15 lbs + 230W:
+ ~15:08 ✓
+
+
+
+
+
+
Recommended Strategy:
+
+ Short term (next attempt): Use a geared bike. Even with the same 214W power, you'll save 1:30-2:00 by avoiding the cadence collapse. Your HR data shows you have more cardiovascular capacity - you just can't access it with that gearing.
+
+
+ Medium term (2-3 months): With gears + focused training to raise sustained power from 214W to 230-245W through sweet spot intervals and VO2max work, 15:08 is very achievable.
+
+
+
+ );
+ };
+
+ export default ClimbPacingCalculator;
+ ````
+- ## Key Findings from Your Detailed Data:
+
+ **The smoking gun is at the 39:00 mark** - your speed collapsed to 7.3 mph while grinding at 46 rpm. This is where you lost most of your time. The data tells a clear story:
+
+ 1. **You started well**: First ~26 minutes averaging 12-13 mph at 70-90 rpm - sustainable pace
+ 2. **Middle section held**: 26-35 minutes still maintaining 11-12 mph, though cadence dropping to 60-80 rpm
+ 3. **The collapse (35-39 minutes)**: Speed crashed to 7.3 mph, cadence dropped to 46 rpm, but HR was only 168 bpm (not maxed at 181)
+ 4. **Critical insight**: Your heart rate shows your cardiovascular system had more to give, but your legs couldn't turn the pedals fast enough in that gear
+
+ **The math is brutal**: At 46 rpm in a 38/20 gear on a 7-8% grade, you're applying massive force per pedal stroke. This fatigues your muscles far faster than spinning at 80-90 rpm with the same power output.
+
+ **Bottom line from the data**:
+- Gearing is costing you 1:30-2:00 minimum (probably more)
+- With proper gears, you could maintain 70+ rpm throughout and likely sustain 230W instead of 214W
+- Combined effect: gears alone could get you to ~16:30-17:00
+- Gears + modest power increase (230-245W) = 15:08 is very achievable
+
+ The good news? Your HR data suggests you have untapped cardiovascular capacity. You just need gearing that lets you access it.
+- ## Prompt:
+ 12/11/2025, 1:45:33 PM
+
+ i have access to other rear cogs 14,16,18,20,22 would any of these be better?
+- ## Response:
+ 12/11/2025, 1:46:57 PM
+
+ Let me analyze which cog would work best for this climb with your 38t chainring.
+
+ **Climb Pacing Strategy Calculator** ∙ Version 6
+
+ ````jsx
+ import React, { useState, useMemo } from 'react';
+ import { LineChart, Line, XAxis, YAxis, CartesianGrid, Tooltip, Legend, ResponsiveContainer } from 'recharts';
+
+ const ClimbPacingCalculator = () => {
+ const [params, setParams] = useState({
+ riderWeight: 203,
+ bikeWeight: 22,
+ CdA: 0.388, // Reasonable default for road position
+ Crr: 0.004, // Good tires on smooth pavement
+ drivetrainLoss: 2,
+ headwind: 0,
+ rho: 0.075, // Air density at sea level (lb/ft^3)
+ targetTime: 908, // 15:08 in seconds
+ actualTime: 1123, // 18:43 actual
+ actualPower: 214, // W average
+ chainring: 38,
+ cog: 20
+ });
+
+ // Convert elevation profile from image to data points
+ const elevationProfile = useMemo(() => {
+ const points = [];
+ const distances = [0, 0.2, 0.4, 0.6, 0.8, 1.0, 1.2, 1.4, 1.6, 1.8, 2.0, 2.2, 2.4, 2.6, 2.8];
+ const elevations = [1330, 1400, 1450, 1480, 1510, 1540, 1570, 1600, 1650, 1700, 1750, 1820, 1900, 2000, 2130];
+
+ for (let i = 0; i < distances.length; i++) {
+ const grade = i > 0
+ ? ((elevations[i] - elevations[i-1]) / (5280 * (distances[i] - distances[i-1]))) * 100
+ : 0;
+ points.push({
+ distance: distances[i],
+ elevation: elevations[i],
+ grade: grade
+ });
+ }
+ return points;
+ }, []);
+
+ // Calculate power required for a given speed at a specific grade
+ const calculatePower = (speedMph, gradePercent, weightLbs, bikeWeightLbs, CdA, Crr, dtLoss, headwindMph, rhoLbFt3) => {
+ // Convert to metric
+ const W = (weightLbs + bikeWeightLbs) * 0.453592; // kg
+ const Vgs = speedMph * 0.44704; // m/s
+ const Vhw = headwindMph * 0.44704; // m/s
+ const G = gradePercent;
+ const rho = rhoLbFt3 * 16.0185; // kg/m^3
+ const CdAMetric = CdA * 0.092903; // m^2
+
+ // Calculate forces
+ const Fgravity = 9.8067 * Math.sin(Math.atan(G / 100)) * W;
+ const Frolling = 9.8067 * Math.cos(Math.atan(G / 100)) * W * Crr;
+ const Vas = Vgs + Vhw;
+ const Fdrag = 0.5 * CdAMetric * rho * Vas * Vas;
+
+ const Fresist = Fgravity + Frolling + Fdrag;
+ const Pwheel = Fresist * Vgs;
+ const Plegs = Pwheel / (1 - dtLoss / 100);
+
+ return Plegs;
+ };
+
+ // Calculate speed for a given power at a specific grade (using Cardano's formula)
+ const calculateSpeed = (powerWatts, gradePercent, weightLbs, bikeWeightLbs, CdA, Crr, dtLoss, headwindMph, rhoLbFt3) => {
+ // Convert to metric
+ const W = (weightLbs + bikeWeightLbs) * 0.453592; // kg
+ const Vhw = headwindMph * 0.44704; // m/s
+ const G = gradePercent;
+ const rho = rhoLbFt3 * 16.0185; // kg/m^3
+ const CdAMetric = CdA * 0.092903; // m^2
+ const P = powerWatts;
+
+ // Cubic equation coefficients
+ const a = 0.5 * CdAMetric * rho;
+ const b = Vhw * CdAMetric * rho;
+ const c = (9.8067 * W * (Math.sin(Math.atan(G / 100)) + Crr * Math.cos(Math.atan(G / 100)))) +
+ (0.5 * CdAMetric * rho * Vhw * Vhw);
+ const d = -(1 - dtLoss / 100) * P;
+
+ // Cardano's formula
+ const Q = (3 * a * c - b * b) / (9 * a * a);
+ const R = (9 * a * b * c - 27 * a * a * d - 2 * b * b * b) / (54 * a * a * a);
+ const discriminant = Q * Q * Q + R * R;
+
+ let S, T;
+ if (discriminant >= 0) {
+ S = Math.cbrt(R + Math.sqrt(discriminant));
+ T = Math.cbrt(R - Math.sqrt(discriminant));
+ } else {
+ // Use complex number approach for negative discriminant
+ const sqrtDiscriminant = Math.sqrt(-discriminant);
+ S = Math.cbrt(Math.sqrt(R * R + discriminant));
+ T = S;
+ }
+
+ const Vgs = S + T - (b / (3 * a));
+ const speedMph = Vgs * 2.23694; // m/s to mph
+
+ return speedMph > 0 ? speedMph : 0;
+ };
+
+ // Generate pacing strategy
+ const pacingStrategy = useMemo(() => {
+ const { riderWeight, bikeWeight, CdA, Crr, drivetrainLoss, headwind, rho, targetTime } = params;
+
+ // Binary search for average power to hit target time
+ let powerLow = 100;
+ let powerHigh = 600;
+ let bestPower = 250;
+ let iterations = 0;
+
+ while (powerHigh - powerLow > 0.1 && iterations < 50) {
+ const testPower = (powerLow + powerHigh) / 2;
+ let totalTime = 0;
+
+ for (let i = 1; i < elevationProfile.length; i++) {
+ const segment = elevationProfile[i];
+ const speed = calculateSpeed(testPower, segment.grade, riderWeight, bikeWeight, CdA, Crr, drivetrainLoss, headwind, rho);
+ const distance = segment.distance - elevationProfile[i-1].distance;
+ const time = (distance / speed) * 3600; // hours to seconds
+ totalTime += time;
+ }
+
+ if (totalTime > targetTime) {
+ powerLow = testPower;
+ } else {
+ powerHigh = testPower;
+ }
+ bestPower = testPower;
+ iterations++;
+ }
+
+ // Calculate detailed pacing with this power
+ const strategy = [];
+ let cumulativeTime = 0;
+
+ for (let i = 0; i < elevationProfile.length; i++) {
+ const segment = elevationProfile[i];
+ const speed = i > 0
+ ? calculateSpeed(bestPower, segment.grade, riderWeight, bikeWeight, CdA, Crr, drivetrainLoss, headwind, rho)
+ : 0;
+
+ const distance = i > 0 ? segment.distance - elevationProfile[i-1].distance : 0;
+ const segmentTime = speed > 0 ? (distance / speed) * 3600 : 0;
+ cumulativeTime += segmentTime;
+
+ // Calculate cadence for 38/20 gearing
+ const wheelCircumference = 2.1; // meters (700c wheel)
+ const gearRatio = 38 / 20;
+ const cadence = speed > 0 ? (speed * 0.44704 * 60) / (wheelCircumference * gearRatio) : 0;
+
+ strategy.push({
+ distance: segment.distance,
+ elevation: segment.elevation,
+ grade: segment.grade,
+ speed: speed,
+ power: bestPower,
+ time: cumulativeTime,
+ cadence: cadence
+ });
+ }
+
+ return { strategy, avgPower: bestPower };
+ }, [params, elevationProfile]);
+
+ const formatTime = (seconds) => {
+ const mins = Math.floor(seconds / 60);
+ const secs = Math.floor(seconds % 60);
+ return `${mins}:${secs.toString().padStart(2, '0')}`;
+ };
+
+ return (
+
+
Climb Pacing Strategy
+
+
+
+
+
+
Target vs Actual
+
+
+
YOUR BEST EFFORT
+
+ Time:
+ 18:43
+
+
+ Avg Power:
+ 214W
+
+
+ Avg Speed:
+ 9.1 mph
+
+
+
+
TARGET (15:08)
+
+ Required Power:
+ {pacingStrategy.avgPower.toFixed(0)}W
+
+
+ Avg Speed:
+
+ {((2.8 / (pacingStrategy.strategy[pacingStrategy.strategy.length - 1]?.time / 3600)) || 0).toFixed(1)} mph
+
+
+
+
+
GAP TO CLOSE
+
+ Time:
+ -3:35 ({((params.actualTime - params.targetTime) / params.actualTime * 100).toFixed(1)}%)
+
+
+ Power:
+ +{(pacingStrategy.avgPower - params.actualPower).toFixed(0)}W ({((pacingStrategy.avgPower - params.actualPower) / params.actualPower * 100).toFixed(1)}%)
+
+
+
+
+
+
+
+
Speed Profile
+
+
+
+
+
+
+
+
+
+
+
+
+
Elevation & Gradient
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
Detailed Pacing Table
+
+
+
+
+ | Distance (mi) |
+ Elevation (ft) |
+ Grade (%) |
+ Speed (mph) |
+ Cadence (rpm) |
+ Power (W) |
+ Time |
+
+
+
+ {pacingStrategy.strategy.map((point, idx) => (
+
+ | {point.distance.toFixed(1)} |
+ {point.elevation.toFixed(0)} |
+ {point.grade.toFixed(1)} |
+ {point.speed.toFixed(1)} |
+ {point.cadence.toFixed(0)} |
+ {point.power.toFixed(0)} |
+ {formatTime(point.time)} |
+
+ ))}
+
+
+
+
+
+
+
Analysis: What Happened in Your Effort
+
+
+
Critical Issue: Speed Collapse at 39:00 mark (around mile 2.3-2.5)
+
Your speed dropped dramatically to ~7.3 mph while HR stayed at 168 bpm and cadence dropped to 46 rpm. This is where you lost significant time - you were grinding at unsustainably low cadence on the steepest section.
+
+
+
+
Pacing Pattern Analysis:
+
+ - Start (0-26:40): Consistent ~12-13 mph, 70-90 rpm cadence, ~150 bpm HR - good sustainable pace
+ - Middle (26:40-35:00): Speed holding ~11-12 mph, cadence still decent 60-80 rpm, HR climbing to 160s
+ - Crisis Point (35:00-39:00): Speed crashes to 7.3 mph, cadence drops to 46 rpm, HR maxed at 168 bpm - you hit the wall on the steepest pitch
+ - Recovery sections (gaps in data): Appears you had to stop/soft pedal briefly, then resumed
+ - Final push (40:00+): HR surged to 135+ but speed didn't recover - too fatigued
+
+
+
+
+
The Singlespeed Problem (38/20 gearing):
+
At 46 rpm on the steep section, you're at 60% of your average cadence. This gear is simply too tall for the 7-8% gradient sections. You're forced to:
+
+ - Mash at very low cadence (high muscular force per pedal stroke)
+ - This fatigues your legs faster than your cardiovascular system
+ - Notice your HR wasn't maxed out (168 bpm vs 181 max) - your legs failed before your cardio did
+
+
+
+
+
Where Time Was Lost:
+
Comparing to target 15:08 pace:
+
+ - First half (miles 0-1.4): Relatively close to target, maybe lost 30-45 seconds
+ - Steep section (miles 1.4-2.8): Lost 2:30-3:00 here due to the speed collapse
+ - The 39:00 mark crisis point alone probably cost 1:30-2:00
+
+
+
+
+
+
+
⚠️ Critical Finding: Gearing is Your Biggest Limiter
+
+
Your data clearly shows the 38/20 singlespeed forced you into an impossible situation on the steep sections. At 214W average power, you should be capable of ~10-11 mph on 7% grades with proper gearing (80-90 rpm). Instead, you were forced to 7.3 mph at 46 rpm.
+
If you had gears allowing you to maintain 70+ rpm throughout:
+
+ - You could likely sustain 230-240W instead of 214W (less muscular fatigue)
+ - You wouldn't have the catastrophic slowdown at 39:00
+ - Estimated time with same 214W but proper gearing: 16:30-17:15
+ - With 230W + proper gearing: 15:30-16:00
+
+
+
+
+
+
Realistic Pathways to 15:08:
+
+
+ Option 1: Switch to gears + maintain current 214W:
+ ~17:00 (not quite there)
+
+
+ Option 2: Switch to gears + increase to 245W:
+ ~15:08 ✓
+
+
+ Option 3: Keep singlespeed + increase to 300W+:
+ ~15:08 (extremely difficult, cadence issues persist)
+
+
+ Option 4: Gears + lose 15 lbs + 230W:
+ ~15:08 ✓
+
+
+
+
+
+
Recommended Strategy:
+
+ Short term (next attempt): Use a geared bike. Even with the same 214W power, you'll save 1:30-2:00 by avoiding the cadence collapse. Your HR data shows you have more cardiovascular capacity - you just can't access it with that gearing.
+
+
+ Medium term (2-3 months): With gears + focused training to raise sustained power from 214W to 230-245W through sweet spot intervals and VO2max work, 15:08 is very achievable.
+
+
+
+ );
+ };
+
+ export default ClimbPacingCalculator;
+ ````
+
+ **Climb Pacing Strategy Calculator** ∙ Version 7
+
+ ````jsx
+ import React, { useState, useMemo } from 'react';
+ import { LineChart, Line, XAxis, YAxis, CartesianGrid, Tooltip, Legend, ResponsiveContainer } from 'recharts';
+
+ const ClimbPacingCalculator = () => {
+ const [params, setParams] = useState({
+ riderWeight: 203,
+ bikeWeight: 22,
+ CdA: 0.388, // Reasonable default for road position
+ Crr: 0.004, // Good tires on smooth pavement
+ drivetrainLoss: 2,
+ headwind: 0,
+ rho: 0.075, // Air density at sea level (lb/ft^3)
+ targetTime: 908, // 15:08 in seconds
+ actualTime: 1123, // 18:43 actual
+ actualPower: 214, // W average
+ chainring: 38,
+ cog: 20
+ });
+
+ // Convert elevation profile from image to data points
+ const elevationProfile = useMemo(() => {
+ const points = [];
+ const distances = [0, 0.2, 0.4, 0.6, 0.8, 1.0, 1.2, 1.4, 1.6, 1.8, 2.0, 2.2, 2.4, 2.6, 2.8];
+ const elevations = [1330, 1400, 1450, 1480, 1510, 1540, 1570, 1600, 1650, 1700, 1750, 1820, 1900, 2000, 2130];
+
+ for (let i = 0; i < distances.length; i++) {
+ const grade = i > 0
+ ? ((elevations[i] - elevations[i-1]) / (5280 * (distances[i] - distances[i-1]))) * 100
+ : 0;
+ points.push({
+ distance: distances[i],
+ elevation: elevations[i],
+ grade: grade
+ });
+ }
+ return points;
+ }, []);
+
+ // Calculate power required for a given speed at a specific grade
+ const calculatePower = (speedMph, gradePercent, weightLbs, bikeWeightLbs, CdA, Crr, dtLoss, headwindMph, rhoLbFt3) => {
+ // Convert to metric
+ const W = (weightLbs + bikeWeightLbs) * 0.453592; // kg
+ const Vgs = speedMph * 0.44704; // m/s
+ const Vhw = headwindMph * 0.44704; // m/s
+ const G = gradePercent;
+ const rho = rhoLbFt3 * 16.0185; // kg/m^3
+ const CdAMetric = CdA * 0.092903; // m^2
+
+ // Calculate forces
+ const Fgravity = 9.8067 * Math.sin(Math.atan(G / 100)) * W;
+ const Frolling = 9.8067 * Math.cos(Math.atan(G / 100)) * W * Crr;
+ const Vas = Vgs + Vhw;
+ const Fdrag = 0.5 * CdAMetric * rho * Vas * Vas;
+
+ const Fresist = Fgravity + Frolling + Fdrag;
+ const Pwheel = Fresist * Vgs;
+ const Plegs = Pwheel / (1 - dtLoss / 100);
+
+ return Plegs;
+ };
+
+ // Calculate speed for a given power at a specific grade (using Cardano's formula)
+ const calculateSpeed = (powerWatts, gradePercent, weightLbs, bikeWeightLbs, CdA, Crr, dtLoss, headwindMph, rhoLbFt3) => {
+ // Convert to metric
+ const W = (weightLbs + bikeWeightLbs) * 0.453592; // kg
+ const Vhw = headwindMph * 0.44704; // m/s
+ const G = gradePercent;
+ const rho = rhoLbFt3 * 16.0185; // kg/m^3
+ const CdAMetric = CdA * 0.092903; // m^2
+ const P = powerWatts;
+
+ // Cubic equation coefficients
+ const a = 0.5 * CdAMetric * rho;
+ const b = Vhw * CdAMetric * rho;
+ const c = (9.8067 * W * (Math.sin(Math.atan(G / 100)) + Crr * Math.cos(Math.atan(G / 100)))) +
+ (0.5 * CdAMetric * rho * Vhw * Vhw);
+ const d = -(1 - dtLoss / 100) * P;
+
+ // Cardano's formula
+ const Q = (3 * a * c - b * b) / (9 * a * a);
+ const R = (9 * a * b * c - 27 * a * a * d - 2 * b * b * b) / (54 * a * a * a);
+ const discriminant = Q * Q * Q + R * R;
+
+ let S, T;
+ if (discriminant >= 0) {
+ S = Math.cbrt(R + Math.sqrt(discriminant));
+ T = Math.cbrt(R - Math.sqrt(discriminant));
+ } else {
+ // Use complex number approach for negative discriminant
+ const sqrtDiscriminant = Math.sqrt(-discriminant);
+ S = Math.cbrt(Math.sqrt(R * R + discriminant));
+ T = S;
+ }
+
+ const Vgs = S + T - (b / (3 * a));
+ const speedMph = Vgs * 2.23694; // m/s to mph
+
+ return speedMph > 0 ? speedMph : 0;
+ };
+
+ // Generate pacing strategy
+ const pacingStrategy = useMemo(() => {
+ const { riderWeight, bikeWeight, CdA, Crr, drivetrainLoss, headwind, rho, targetTime } = params;
+
+ // Binary search for average power to hit target time
+ let powerLow = 100;
+ let powerHigh = 600;
+ let bestPower = 250;
+ let iterations = 0;
+
+ while (powerHigh - powerLow > 0.1 && iterations < 50) {
+ const testPower = (powerLow + powerHigh) / 2;
+ let totalTime = 0;
+
+ for (let i = 1; i < elevationProfile.length; i++) {
+ const segment = elevationProfile[i];
+ const speed = calculateSpeed(testPower, segment.grade, riderWeight, bikeWeight, CdA, Crr, drivetrainLoss, headwind, rho);
+ const distance = segment.distance - elevationProfile[i-1].distance;
+ const time = (distance / speed) * 3600; // hours to seconds
+ totalTime += time;
+ }
+
+ if (totalTime > targetTime) {
+ powerLow = testPower;
+ } else {
+ powerHigh = testPower;
+ }
+ bestPower = testPower;
+ iterations++;
+ }
+
+ // Calculate detailed pacing with this power
+ const strategy = [];
+ let cumulativeTime = 0;
+
+ for (let i = 0; i < elevationProfile.length; i++) {
+ const segment = elevationProfile[i];
+ const speed = i > 0
+ ? calculateSpeed(bestPower, segment.grade, riderWeight, bikeWeight, CdA, Crr, drivetrainLoss, headwind, rho)
+ : 0;
+
+ const distance = i > 0 ? segment.distance - elevationProfile[i-1].distance : 0;
+ const segmentTime = speed > 0 ? (distance / speed) * 3600 : 0;
+ cumulativeTime += segmentTime;
+
+ // Calculate cadence for selected gearing
+ const wheelCircumference = 2.1; // meters (700c wheel)
+ const gearRatio = params.chainring / params.cog;
+ const cadence = speed > 0 ? (speed * 0.44704 * 60) / (wheelCircumference * gearRatio) : 0;
+
+ strategy.push({
+ distance: segment.distance,
+ elevation: segment.elevation,
+ grade: segment.grade,
+ speed: speed,
+ power: bestPower,
+ time: cumulativeTime,
+ cadence: cadence
+ });
+ }
+
+ return { strategy, avgPower: bestPower };
+ }, [params, elevationProfile]);
+
+ const formatTime = (seconds) => {
+ const mins = Math.floor(seconds / 60);
+ const secs = Math.floor(seconds % 60);
+ return `${mins}:${secs.toString().padStart(2, '0')}`;
+ };
+
+ return (
+
+
Climb Pacing Strategy
+
+
+
+
+
+
Target vs Actual
+
+
+
YOUR BEST EFFORT
+
+ Time:
+ 18:43
+
+
+ Avg Power:
+ 214W
+
+
+ Avg Speed:
+ 9.1 mph
+
+
+
+
TARGET (15:08)
+
+ Required Power:
+ {pacingStrategy.avgPower.toFixed(0)}W
+
+
+ Avg Speed:
+
+ {((2.8 / (pacingStrategy.strategy[pacingStrategy.strategy.length - 1]?.time / 3600)) || 0).toFixed(1)} mph
+
+
+
+
+
GAP TO CLOSE
+
+ Time:
+ -3:35 ({((params.actualTime - params.targetTime) / params.actualTime * 100).toFixed(1)}%)
+
+
+ Power:
+ +{(pacingStrategy.avgPower - params.actualPower).toFixed(0)}W ({((pacingStrategy.avgPower - params.actualPower) / params.actualPower * 100).toFixed(1)}%)
+
+
+
+
+
+
+
+
Speed Profile
+
+
+
+
+
+
+
+
+
+
+
+
+
Elevation & Gradient
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
Detailed Pacing Table
+
+
+
+
+ | Distance (mi) |
+ Elevation (ft) |
+ Grade (%) |
+ Speed (mph) |
+ Cadence (rpm) |
+ Power (W) |
+ Time |
+
+
+
+ {pacingStrategy.strategy.map((point, idx) => (
+
+ | {point.distance.toFixed(1)} |
+ {point.elevation.toFixed(0)} |
+ {point.grade.toFixed(1)} |
+ {point.speed.toFixed(1)} |
+ {point.cadence.toFixed(0)} |
+ {point.power.toFixed(0)} |
+ {formatTime(point.time)} |
+
+ ))}
+
+
+
+
+
+
+
Analysis: What Happened in Your Effort
+
+
+
Critical Issue: Speed Collapse at 39:00 mark (around mile 2.3-2.5)
+
Your speed dropped dramatically to ~7.3 mph while HR stayed at 168 bpm and cadence dropped to 46 rpm. This is where you lost significant time - you were grinding at unsustainably low cadence on the steepest section.
+
+
+
+
Pacing Pattern Analysis:
+
+ - Start (0-26:40): Consistent ~12-13 mph, 70-90 rpm cadence, ~150 bpm HR - good sustainable pace
+ - Middle (26:40-35:00): Speed holding ~11-12 mph, cadence still decent 60-80 rpm, HR climbing to 160s
+ - Crisis Point (35:00-39:00): Speed crashes to 7.3 mph, cadence drops to 46 rpm, HR maxed at 168 bpm - you hit the wall on the steepest pitch
+ - Recovery sections (gaps in data): Appears you had to stop/soft pedal briefly, then resumed
+ - Final push (40:00+): HR surged to 135+ but speed didn't recover - too fatigued
+
+
+
+
+
The Singlespeed Problem (38/20 gearing):
+
At 46 rpm on the steep section, you're at 60% of your average cadence. This gear is simply too tall for the 7-8% gradient sections. You're forced to:
+
+ - Mash at very low cadence (high muscular force per pedal stroke)
+ - This fatigues your legs faster than your cardiovascular system
+ - Notice your HR wasn't maxed out (168 bpm vs 181 max) - your legs failed before your cardio did
+
+
+
+
+
Where Time Was Lost:
+
Comparing to target 15:08 pace:
+
+ - First half (miles 0-1.4): Relatively close to target, maybe lost 30-45 seconds
+ - Steep section (miles 1.4-2.8): Lost 2:30-3:00 here due to the speed collapse
+ - The 39:00 mark crisis point alone probably cost 1:30-2:00
+
+
+
+
+
+
+
⚠️ Critical Finding: Gearing is Your Biggest Limiter
+
+
Your data clearly shows the 38/20 singlespeed forced you into an impossible situation on the steep sections. At 214W average power, you should be capable of ~10-11 mph on 7% grades with proper gearing (80-90 rpm). Instead, you were forced to 7.3 mph at 46 rpm.
+
If you had gears allowing you to maintain 70+ rpm throughout:
+
+ - You could likely sustain 230-240W instead of 214W (less muscular fatigue)
+ - You wouldn't have the catastrophic slowdown at 39:00
+ - Estimated time with same 214W but proper gearing: 16:30-17:15
+ - With 230W + proper gearing: 15:30-16:00
+
+
+
+
+
+
Realistic Pathways to 15:08:
+
+
+ Option 1: Switch to gears + maintain current 214W:
+ ~17:00 (not quite there)
+
+
+ Option 2: Switch to gears + increase to 245W:
+ ~15:08 ✓
+
+
+ Option 3: Keep singlespeed + increase to 300W+:
+ ~15:08 (extremely difficult, cadence issues persist)
+
+
+ Option 4: Gears + lose 15 lbs + 230W:
+ ~15:08 ✓
+
+
+
+
+
+
Recommended Strategy:
+
+ Short term (next attempt): Use a geared bike. Even with the same 214W power, you'll save 1:30-2:00 by avoiding the cadence collapse. Your HR data shows you have more cardiovascular capacity - you just can't access it with that gearing.
+
+
+ Medium term (2-3 months): With gears + focused training to raise sustained power from 214W to 230-245W through sweet spot intervals and VO2max work, 15:08 is very achievable.
+
+
+
+ );
+ };
+
+ export default ClimbPacingCalculator;
+ ````
+
+ **Climb Pacing Strategy Calculator** ∙ Version 8
+
+ ````jsx
+ import React, { useState, useMemo } from 'react';
+ import { LineChart, Line, XAxis, YAxis, CartesianGrid, Tooltip, Legend, ResponsiveContainer } from 'recharts';
+
+ const ClimbPacingCalculator = () => {
+ const [params, setParams] = useState({
+ riderWeight: 203,
+ bikeWeight: 22,
+ CdA: 0.388, // Reasonable default for road position
+ Crr: 0.004, // Good tires on smooth pavement
+ drivetrainLoss: 2,
+ headwind: 0,
+ rho: 0.075, // Air density at sea level (lb/ft^3)
+ targetTime: 908, // 15:08 in seconds
+ actualTime: 1123, // 18:43 actual
+ actualPower: 214, // W average
+ chainring: 38,
+ cog: 20
+ });
+
+ // Convert elevation profile from image to data points
+ const elevationProfile = useMemo(() => {
+ const points = [];
+ const distances = [0, 0.2, 0.4, 0.6, 0.8, 1.0, 1.2, 1.4, 1.6, 1.8, 2.0, 2.2, 2.4, 2.6, 2.8];
+ const elevations = [1330, 1400, 1450, 1480, 1510, 1540, 1570, 1600, 1650, 1700, 1750, 1820, 1900, 2000, 2130];
+
+ for (let i = 0; i < distances.length; i++) {
+ const grade = i > 0
+ ? ((elevations[i] - elevations[i-1]) / (5280 * (distances[i] - distances[i-1]))) * 100
+ : 0;
+ points.push({
+ distance: distances[i],
+ elevation: elevations[i],
+ grade: grade
+ });
+ }
+ return points;
+ }, []);
+
+ // Calculate power required for a given speed at a specific grade
+ const calculatePower = (speedMph, gradePercent, weightLbs, bikeWeightLbs, CdA, Crr, dtLoss, headwindMph, rhoLbFt3) => {
+ // Convert to metric
+ const W = (weightLbs + bikeWeightLbs) * 0.453592; // kg
+ const Vgs = speedMph * 0.44704; // m/s
+ const Vhw = headwindMph * 0.44704; // m/s
+ const G = gradePercent;
+ const rho = rhoLbFt3 * 16.0185; // kg/m^3
+ const CdAMetric = CdA * 0.092903; // m^2
+
+ // Calculate forces
+ const Fgravity = 9.8067 * Math.sin(Math.atan(G / 100)) * W;
+ const Frolling = 9.8067 * Math.cos(Math.atan(G / 100)) * W * Crr;
+ const Vas = Vgs + Vhw;
+ const Fdrag = 0.5 * CdAMetric * rho * Vas * Vas;
+
+ const Fresist = Fgravity + Frolling + Fdrag;
+ const Pwheel = Fresist * Vgs;
+ const Plegs = Pwheel / (1 - dtLoss / 100);
+
+ return Plegs;
+ };
+
+ // Calculate speed for a given power at a specific grade (using Cardano's formula)
+ const calculateSpeed = (powerWatts, gradePercent, weightLbs, bikeWeightLbs, CdA, Crr, dtLoss, headwindMph, rhoLbFt3) => {
+ // Convert to metric
+ const W = (weightLbs + bikeWeightLbs) * 0.453592; // kg
+ const Vhw = headwindMph * 0.44704; // m/s
+ const G = gradePercent;
+ const rho = rhoLbFt3 * 16.0185; // kg/m^3
+ const CdAMetric = CdA * 0.092903; // m^2
+ const P = powerWatts;
+
+ // Cubic equation coefficients
+ const a = 0.5 * CdAMetric * rho;
+ const b = Vhw * CdAMetric * rho;
+ const c = (9.8067 * W * (Math.sin(Math.atan(G / 100)) + Crr * Math.cos(Math.atan(G / 100)))) +
+ (0.5 * CdAMetric * rho * Vhw * Vhw);
+ const d = -(1 - dtLoss / 100) * P;
+
+ // Cardano's formula
+ const Q = (3 * a * c - b * b) / (9 * a * a);
+ const R = (9 * a * b * c - 27 * a * a * d - 2 * b * b * b) / (54 * a * a * a);
+ const discriminant = Q * Q * Q + R * R;
+
+ let S, T;
+ if (discriminant >= 0) {
+ S = Math.cbrt(R + Math.sqrt(discriminant));
+ T = Math.cbrt(R - Math.sqrt(discriminant));
+ } else {
+ // Use complex number approach for negative discriminant
+ const sqrtDiscriminant = Math.sqrt(-discriminant);
+ S = Math.cbrt(Math.sqrt(R * R + discriminant));
+ T = S;
+ }
+
+ const Vgs = S + T - (b / (3 * a));
+ const speedMph = Vgs * 2.23694; // m/s to mph
+
+ return speedMph > 0 ? speedMph : 0;
+ };
+
+ // Generate pacing strategy
+ const pacingStrategy = useMemo(() => {
+ const { riderWeight, bikeWeight, CdA, Crr, drivetrainLoss, headwind, rho, targetTime } = params;
+
+ // Binary search for average power to hit target time
+ let powerLow = 100;
+ let powerHigh = 600;
+ let bestPower = 250;
+ let iterations = 0;
+
+ while (powerHigh - powerLow > 0.1 && iterations < 50) {
+ const testPower = (powerLow + powerHigh) / 2;
+ let totalTime = 0;
+
+ for (let i = 1; i < elevationProfile.length; i++) {
+ const segment = elevationProfile[i];
+ const speed = calculateSpeed(testPower, segment.grade, riderWeight, bikeWeight, CdA, Crr, drivetrainLoss, headwind, rho);
+ const distance = segment.distance - elevationProfile[i-1].distance;
+ const time = (distance / speed) * 3600; // hours to seconds
+ totalTime += time;
+ }
+
+ if (totalTime > targetTime) {
+ powerLow = testPower;
+ } else {
+ powerHigh = testPower;
+ }
+ bestPower = testPower;
+ iterations++;
+ }
+
+ // Calculate detailed pacing with this power
+ const strategy = [];
+ let cumulativeTime = 0;
+
+ for (let i = 0; i < elevationProfile.length; i++) {
+ const segment = elevationProfile[i];
+ const speed = i > 0
+ ? calculateSpeed(bestPower, segment.grade, riderWeight, bikeWeight, CdA, Crr, drivetrainLoss, headwind, rho)
+ : 0;
+
+ const distance = i > 0 ? segment.distance - elevationProfile[i-1].distance : 0;
+ const segmentTime = speed > 0 ? (distance / speed) * 3600 : 0;
+ cumulativeTime += segmentTime;
+
+ // Calculate cadence for selected gearing
+ const wheelCircumference = 2.1; // meters (700c wheel)
+ const gearRatio = params.chainring / params.cog;
+ const cadence = speed > 0 ? (speed * 0.44704 * 60) / (wheelCircumference * gearRatio) : 0;
+
+ strategy.push({
+ distance: segment.distance,
+ elevation: segment.elevation,
+ grade: segment.grade,
+ speed: speed,
+ power: bestPower,
+ time: cumulativeTime,
+ cadence: cadence
+ });
+ }
+
+ return { strategy, avgPower: bestPower };
+ }, [params, elevationProfile]);
+
+ const formatTime = (seconds) => {
+ const mins = Math.floor(seconds / 60);
+ const secs = Math.floor(seconds % 60);
+ return `${mins}:${secs.toString().padStart(2, '0')}`;
+ };
+
+ return (
+
+
Climb Pacing Strategy
+
+
+
+
+
+
Target vs Actual
+
+
+
YOUR BEST EFFORT
+
+ Time:
+ 18:43
+
+
+ Avg Power:
+ 214W
+
+
+ Avg Speed:
+ 9.1 mph
+
+
+
+
TARGET (15:08)
+
+ Required Power:
+ {pacingStrategy.avgPower.toFixed(0)}W
+
+
+ Avg Speed:
+
+ {((2.8 / (pacingStrategy.strategy[pacingStrategy.strategy.length - 1]?.time / 3600)) || 0).toFixed(1)} mph
+
+
+
+
+
GAP TO CLOSE
+
+ Time:
+ -3:35 ({((params.actualTime - params.targetTime) / params.actualTime * 100).toFixed(1)}%)
+
+
+ Power:
+ +{(pacingStrategy.avgPower - params.actualPower).toFixed(0)}W ({((pacingStrategy.avgPower - params.actualPower) / params.actualPower * 100).toFixed(1)}%)
+
+
+
+
+
+
+
+
Speed Profile
+
+
+
+
+
+
+
+
+
+
+
+
+
Elevation & Gradient
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
Detailed Pacing Table
+
+
+
+
+ | Distance (mi) |
+ Elevation (ft) |
+ Grade (%) |
+ Speed (mph) |
+ Cadence (rpm) |
+ Power (W) |
+ Time |
+
+
+
+ {pacingStrategy.strategy.map((point, idx) => (
+
+ | {point.distance.toFixed(1)} |
+ {point.elevation.toFixed(0)} |
+ {point.grade.toFixed(1)} |
+ {point.speed.toFixed(1)} |
+ {point.cadence.toFixed(0)} |
+ {point.power.toFixed(0)} |
+ {formatTime(point.time)} |
+
+ ))}
+
+
+
+
+
+
+
Analysis: What Happened in Your Effort
+
+
+
Critical Issue: Speed Collapse at 39:00 mark (around mile 2.3-2.5)
+
Your speed dropped dramatically to ~7.3 mph while HR stayed at 168 bpm and cadence dropped to 46 rpm. This is where you lost significant time - you were grinding at unsustainably low cadence on the steepest section.
+
+
+
+
Pacing Pattern Analysis:
+
+ - Start (0-26:40): Consistent ~12-13 mph, 70-90 rpm cadence, ~150 bpm HR - good sustainable pace
+ - Middle (26:40-35:00): Speed holding ~11-12 mph, cadence still decent 60-80 rpm, HR climbing to 160s
+ - Crisis Point (35:00-39:00): Speed crashes to 7.3 mph, cadence drops to 46 rpm, HR maxed at 168 bpm - you hit the wall on the steepest pitch
+ - Recovery sections (gaps in data): Appears you had to stop/soft pedal briefly, then resumed
+ - Final push (40:00+): HR surged to 135+ but speed didn't recover - too fatigued
+
+
+
+
+
The Singlespeed Problem (38/20 gearing):
+
At 46 rpm on the steep section, you're at 60% of your average cadence. This gear is simply too tall for the 7-8% gradient sections. You're forced to:
+
+ - Mash at very low cadence (high muscular force per pedal stroke)
+ - This fatigues your legs faster than your cardiovascular system
+ - Notice your HR wasn't maxed out (168 bpm vs 181 max) - your legs failed before your cardio did
+
+
+
+
+
Where Time Was Lost:
+
Comparing to target 15:08 pace:
+
+ - First half (miles 0-1.4): Relatively close to target, maybe lost 30-45 seconds
+ - Steep section (miles 1.4-2.8): Lost 2:30-3:00 here due to the speed collapse
+ - The 39:00 mark crisis point alone probably cost 1:30-2:00
+
+
+
+
+
+
+
⚠️ Critical Finding: Gearing is Your Biggest Limiter
+
+
Your data clearly shows the 38/20 singlespeed forced you into an impossible situation on the steep sections. At 214W average power, you should be capable of ~10-11 mph on 7% grades with proper gearing (80-90 rpm). Instead, you were forced to 7.3 mph at 46 rpm.
+
If you had gears allowing you to maintain 70+ rpm throughout:
+
+ - You could likely sustain 230-240W instead of 214W (less muscular fatigue)
+ - You wouldn't have the catastrophic slowdown at 39:00
+ - Estimated time with same 214W but proper gearing: 16:30-17:15
+ - With 230W + proper gearing: 15:30-16:00
+
+
+
+
+
+
Realistic Pathways to 15:08:
+
+
+ Option 1: Switch to gears + maintain current 214W:
+ ~17:00 (not quite there)
+
+
+ Option 2: Switch to gears + increase to 245W:
+ ~15:08 ✓
+
+
+ Option 3: Keep singlespeed + increase to 300W+:
+ ~15:08 (extremely difficult, cadence issues persist)
+
+
+ Option 4: Gears + lose 15 lbs + 230W:
+ ~15:08 ✓
+
+
+
+
+
+
Recommended Strategy:
+
+ Short term (next attempt): Use a geared bike. Even with the same 214W power, you'll save 1:30-2:00 by avoiding the cadence collapse. Your HR data shows you have more cardiovascular capacity - you just can't access it with that gearing.
+
+
+ Medium term (2-3 months): With gears + focused training to raise sustained power from 214W to 230-245W through sweet spot intervals and VO2max work, 15:08 is very achievable.
+
+
+
+ );
+ };
+
+ export default ClimbPacingCalculator;
+ ````
+
+ **Climb Pacing Strategy Calculator** ∙ Version 9
+
+ ````jsx
+ import React, { useState, useMemo } from 'react';
+ import { LineChart, Line, XAxis, YAxis, CartesianGrid, Tooltip, Legend, ResponsiveContainer } from 'recharts';
+
+ const ClimbPacingCalculator = () => {
+ const [params, setParams] = useState({
+ riderWeight: 203,
+ bikeWeight: 22,
+ CdA: 0.388, // Reasonable default for road position
+ Crr: 0.004, // Good tires on smooth pavement
+ drivetrainLoss: 2,
+ headwind: 0,
+ rho: 0.075, // Air density at sea level (lb/ft^3)
+ targetTime: 908, // 15:08 in seconds
+ actualTime: 1123, // 18:43 actual
+ actualPower: 214, // W average
+ chainring: 38,
+ cog: 20
+ });
+
+ // Convert elevation profile from image to data points
+ const elevationProfile = useMemo(() => {
+ const points = [];
+ const distances = [0, 0.2, 0.4, 0.6, 0.8, 1.0, 1.2, 1.4, 1.6, 1.8, 2.0, 2.2, 2.4, 2.6, 2.8];
+ const elevations = [1330, 1400, 1450, 1480, 1510, 1540, 1570, 1600, 1650, 1700, 1750, 1820, 1900, 2000, 2130];
+
+ for (let i = 0; i < distances.length; i++) {
+ const grade = i > 0
+ ? ((elevations[i] - elevations[i-1]) / (5280 * (distances[i] - distances[i-1]))) * 100
+ : 0;
+ points.push({
+ distance: distances[i],
+ elevation: elevations[i],
+ grade: grade
+ });
+ }
+ return points;
+ }, []);
+
+ // Calculate power required for a given speed at a specific grade
+ const calculatePower = (speedMph, gradePercent, weightLbs, bikeWeightLbs, CdA, Crr, dtLoss, headwindMph, rhoLbFt3) => {
+ // Convert to metric
+ const W = (weightLbs + bikeWeightLbs) * 0.453592; // kg
+ const Vgs = speedMph * 0.44704; // m/s
+ const Vhw = headwindMph * 0.44704; // m/s
+ const G = gradePercent;
+ const rho = rhoLbFt3 * 16.0185; // kg/m^3
+ const CdAMetric = CdA * 0.092903; // m^2
+
+ // Calculate forces
+ const Fgravity = 9.8067 * Math.sin(Math.atan(G / 100)) * W;
+ const Frolling = 9.8067 * Math.cos(Math.atan(G / 100)) * W * Crr;
+ const Vas = Vgs + Vhw;
+ const Fdrag = 0.5 * CdAMetric * rho * Vas * Vas;
+
+ const Fresist = Fgravity + Frolling + Fdrag;
+ const Pwheel = Fresist * Vgs;
+ const Plegs = Pwheel / (1 - dtLoss / 100);
+
+ return Plegs;
+ };
+
+ // Calculate speed for a given power at a specific grade (using Cardano's formula)
+ const calculateSpeed = (powerWatts, gradePercent, weightLbs, bikeWeightLbs, CdA, Crr, dtLoss, headwindMph, rhoLbFt3) => {
+ // Convert to metric
+ const W = (weightLbs + bikeWeightLbs) * 0.453592; // kg
+ const Vhw = headwindMph * 0.44704; // m/s
+ const G = gradePercent;
+ const rho = rhoLbFt3 * 16.0185; // kg/m^3
+ const CdAMetric = CdA * 0.092903; // m^2
+ const P = powerWatts;
+
+ // Cubic equation coefficients
+ const a = 0.5 * CdAMetric * rho;
+ const b = Vhw * CdAMetric * rho;
+ const c = (9.8067 * W * (Math.sin(Math.atan(G / 100)) + Crr * Math.cos(Math.atan(G / 100)))) +
+ (0.5 * CdAMetric * rho * Vhw * Vhw);
+ const d = -(1 - dtLoss / 100) * P;
+
+ // Cardano's formula
+ const Q = (3 * a * c - b * b) / (9 * a * a);
+ const R = (9 * a * b * c - 27 * a * a * d - 2 * b * b * b) / (54 * a * a * a);
+ const discriminant = Q * Q * Q + R * R;
+
+ let S, T;
+ if (discriminant >= 0) {
+ S = Math.cbrt(R + Math.sqrt(discriminant));
+ T = Math.cbrt(R - Math.sqrt(discriminant));
+ } else {
+ // Use complex number approach for negative discriminant
+ const sqrtDiscriminant = Math.sqrt(-discriminant);
+ S = Math.cbrt(Math.sqrt(R * R + discriminant));
+ T = S;
+ }
+
+ const Vgs = S + T - (b / (3 * a));
+ const speedMph = Vgs * 2.23694; // m/s to mph
+
+ return speedMph > 0 ? speedMph : 0;
+ };
+
+ // Generate pacing strategy
+ const pacingStrategy = useMemo(() => {
+ const { riderWeight, bikeWeight, CdA, Crr, drivetrainLoss, headwind, rho, targetTime } = params;
+
+ // Binary search for average power to hit target time
+ let powerLow = 100;
+ let powerHigh = 600;
+ let bestPower = 250;
+ let iterations = 0;
+
+ while (powerHigh - powerLow > 0.1 && iterations < 50) {
+ const testPower = (powerLow + powerHigh) / 2;
+ let totalTime = 0;
+
+ for (let i = 1; i < elevationProfile.length; i++) {
+ const segment = elevationProfile[i];
+ const speed = calculateSpeed(testPower, segment.grade, riderWeight, bikeWeight, CdA, Crr, drivetrainLoss, headwind, rho);
+ const distance = segment.distance - elevationProfile[i-1].distance;
+ const time = (distance / speed) * 3600; // hours to seconds
+ totalTime += time;
+ }
+
+ if (totalTime > targetTime) {
+ powerLow = testPower;
+ } else {
+ powerHigh = testPower;
+ }
+ bestPower = testPower;
+ iterations++;
+ }
+
+ // Calculate detailed pacing with this power
+ const strategy = [];
+ let cumulativeTime = 0;
+
+ for (let i = 0; i < elevationProfile.length; i++) {
+ const segment = elevationProfile[i];
+ const speed = i > 0
+ ? calculateSpeed(bestPower, segment.grade, riderWeight, bikeWeight, CdA, Crr, drivetrainLoss, headwind, rho)
+ : 0;
+
+ const distance = i > 0 ? segment.distance - elevationProfile[i-1].distance : 0;
+ const segmentTime = speed > 0 ? (distance / speed) * 3600 : 0;
+ cumulativeTime += segmentTime;
+
+ // Calculate cadence for selected gearing
+ const wheelCircumference = 2.1; // meters (700c wheel)
+ const gearRatio = params.chainring / params.cog;
+ const cadence = speed > 0 ? (speed * 0.44704 * 60) / (wheelCircumference * gearRatio) : 0;
+
+ strategy.push({
+ distance: segment.distance,
+ elevation: segment.elevation,
+ grade: segment.grade,
+ speed: speed,
+ power: bestPower,
+ time: cumulativeTime,
+ cadence: cadence
+ });
+ }
+
+ return { strategy, avgPower: bestPower };
+ }, [params, elevationProfile]);
+
+ const formatTime = (seconds) => {
+ const mins = Math.floor(seconds / 60);
+ const secs = Math.floor(seconds % 60);
+ return `${mins}:${secs.toString().padStart(2, '0')}`;
+ };
+
+ // Generate gear comparison analysis
+ const gearComparison = useMemo(() => {
+ const cogs = [14, 16, 18, 20, 22];
+ const { riderWeight, bikeWeight, CdA, Crr, drivetrainLoss, headwind, rho, actualPower, chainring } = params;
+
+ return cogs.map(cog => {
+ const gearRatio = chainring / cog;
+ const wheelCircumference = 2.1;
+
+ // Calculate performance at different gradient sections
+ const gradients = [3, 5, 7, 8]; // Representative gradients
+ const results = gradients.map(grade => {
+ const speed = calculateSpeed(actualPower, grade, riderWeight, bikeWeight, CdA, Crr, drivetrainLoss, headwind, rho);
+ const cadence = (speed * 0.44704 * 60) / (wheelCircumference * gearRatio);
+ return { grade, speed, cadence };
+ });
+
+ // Calculate overall time estimate
+ let totalTime = 0;
+ for (let i = 1; i < elevationProfile.length; i++) {
+ const segment = elevationProfile[i];
+ const speed = calculateSpeed(actualPower, segment.grade, riderWeight, bikeWeight, CdA, Crr, drivetrainLoss, headwind, rho);
+ const distance = segment.distance - elevationProfile[i-1].distance;
+ const time = (distance / speed) * 3600;
+ totalTime += time;
+ }
+
+ const avgCadence = results.reduce((sum, r) => sum + r.cadence, 0) / results.length;
+ const minCadence = Math.min(...results.map(r => r.cadence));
+
+ return {
+ cog,
+ gearRatio,
+ results,
+ totalTime,
+ avgCadence,
+ minCadence,
+ isCurrent: cog === params.cog
+ };
+ });
+ }, [params, elevationProfile, calculateSpeed]);
+
+ return (
+
+
Climb Pacing Strategy
+
+ {/* Gear comparison section */}
+
+
Gear Comparison (38t chainring with your available cogs)
+
All calculated at your actual 214W power. Shows cadence at different gradients and estimated total time.
+
+
+
+
+
+ | Cog |
+ Ratio |
+ Cadence @ 3% |
+ Cadence @ 5% |
+ Cadence @ 7% |
+ Cadence @ 8% |
+ Min Cadence |
+ Est. Time |
+ vs Current |
+
+
+
+ {gearComparison.map((gear) => (
+ = 60 && gear.minCadence <= 90 ? 'bg-green-50' : 'bg-white'}>
+ |
+ {gear.cog}t {gear.isCurrent && '(current)'}
+ |
+ {gear.gearRatio.toFixed(2)} |
+ {gear.results[0].cadence.toFixed(0)} rpm |
+ {gear.results[1].cadence.toFixed(0)} rpm |
+ {gear.results[2].cadence.toFixed(0)} rpm |
+ {gear.results[3].cadence.toFixed(0)} rpm |
+ {gear.minCadence.toFixed(0)} rpm |
+ {formatTime(gear.totalTime)} |
+
+ {gear.isCurrent ? '—' : (
+
+ {gear.totalTime < params.actualTime ? '-' : '+'}{formatTime(Math.abs(gear.totalTime - params.actualTime))}
+
+ )}
+ |
+
+ ))}
+
+
+
+
+
+
✓ Green highlighted rows = optimal cadence range (60-90 rpm minimum)
+
The gear that keeps you in this range on the steepest sections will be most efficient.
+
+
+
+
+
+
+
+
Target vs Actual
+
+
+
YOUR BEST EFFORT
+
+ Time:
+ 18:43
+
+
+ Avg Power:
+ 214W
+
+
+ Avg Speed:
+ 9.1 mph
+
+
+
+
TARGET (15:08)
+
+ Required Power:
+ {pacingStrategy.avgPower.toFixed(0)}W
+
+
+ Avg Speed:
+
+ {((2.8 / (pacingStrategy.strategy[pacingStrategy.strategy.length - 1]?.time / 3600)) || 0).toFixed(1)} mph
+
+
+
+
+
GAP TO CLOSE
+
+ Time:
+ -3:35 ({((params.actualTime - params.targetTime) / params.actualTime * 100).toFixed(1)}%)
+
+
+ Power:
+ +{(pacingStrategy.avgPower - params.actualPower).toFixed(0)}W ({((pacingStrategy.avgPower - params.actualPower) / params.actualPower * 100).toFixed(1)}%)
+
+
+
+
+
+
+
+
Speed Profile
+
+
+
+
+
+
+
+
+
+
+
+
+
Elevation & Gradient
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
Detailed Pacing Table
+
+
+
+
+ | Distance (mi) |
+ Elevation (ft) |
+ Grade (%) |
+ Speed (mph) |
+ Cadence (rpm) |
+ Power (W) |
+ Time |
+
+
+
+ {pacingStrategy.strategy.map((point, idx) => (
+
+ | {point.distance.toFixed(1)} |
+ {point.elevation.toFixed(0)} |
+ {point.grade.toFixed(1)} |
+ {point.speed.toFixed(1)} |
+ {point.cadence.toFixed(0)} |
+ {point.power.toFixed(0)} |
+ {formatTime(point.time)} |
+
+ ))}
+
+
+
+
+
+
+
Analysis: What Happened in Your Effort
+
+
+
Critical Issue: Speed Collapse at 39:00 mark (around mile 2.3-2.5)
+
Your speed dropped dramatically to ~7.3 mph while HR stayed at 168 bpm and cadence dropped to 46 rpm. This is where you lost significant time - you were grinding at unsustainably low cadence on the steepest section.
+
+
+
+
Pacing Pattern Analysis:
+
+ - Start (0-26:40): Consistent ~12-13 mph, 70-90 rpm cadence, ~150 bpm HR - good sustainable pace
+ - Middle (26:40-35:00): Speed holding ~11-12 mph, cadence still decent 60-80 rpm, HR climbing to 160s
+ - Crisis Point (35:00-39:00): Speed crashes to 7.3 mph, cadence drops to 46 rpm, HR maxed at 168 bpm - you hit the wall on the steepest pitch
+ - Recovery sections (gaps in data): Appears you had to stop/soft pedal briefly, then resumed
+ - Final push (40:00+): HR surged to 135+ but speed didn't recover - too fatigued
+
+
+
+
+
The Singlespeed Problem (38/20 gearing):
+
At 46 rpm on the steep section, you're at 60% of your average cadence. This gear is simply too tall for the 7-8% gradient sections. You're forced to:
+
+ - Mash at very low cadence (high muscular force per pedal stroke)
+ - This fatigues your legs faster than your cardiovascular system
+ - Notice your HR wasn't maxed out (168 bpm vs 181 max) - your legs failed before your cardio did
+
+
+
+
+
Where Time Was Lost:
+
Comparing to target 15:08 pace:
+
+ - First half (miles 0-1.4): Relatively close to target, maybe lost 30-45 seconds
+ - Steep section (miles 1.4-2.8): Lost 2:30-3:00 here due to the speed collapse
+ - The 39:00 mark crisis point alone probably cost 1:30-2:00
+
+
+
+
+
+
+
⚠️ Critical Finding: Gearing is Your Biggest Limiter
+
+
Your data clearly shows the 38/20 singlespeed forced you into an impossible situation on the steep sections. At 214W average power, you should be capable of ~10-11 mph on 7% grades with proper gearing (80-90 rpm). Instead, you were forced to 7.3 mph at 46 rpm.
+
If you had gears allowing you to maintain 70+ rpm throughout:
+
+ - You could likely sustain 230-240W instead of 214W (less muscular fatigue)
+ - You wouldn't have the catastrophic slowdown at 39:00
+ - Estimated time with same 214W but proper gearing: 16:30-17:15
+ - With 230W + proper gearing: 15:30-16:00
+
+
+
+
+
+
Realistic Pathways to 15:08:
+
+
+ Option 1: Switch to gears + maintain current 214W:
+ ~17:00 (not quite there)
+
+
+ Option 2: Switch to gears + increase to 245W:
+ ~15:08 ✓
+
+
+ Option 3: Keep singlespeed + increase to 300W+:
+ ~15:08 (extremely difficult, cadence issues persist)
+
+
+ Option 4: Gears + lose 15 lbs + 230W:
+ ~15:08 ✓
+
+
+
+
+
+
Recommended Strategy:
+
+ Short term (next attempt): Use a geared bike. Even with the same 214W power, you'll save 1:30-2:00 by avoiding the cadence collapse. Your HR data shows you have more cardiovascular capacity - you just can't access it with that gearing.
+
+
+ Medium term (2-3 months): With gears + focused training to raise sustained power from 214W to 230-245W through sweet spot intervals and VO2max work, 15:08 is very achievable.
+
+
+
+ );
+ };
+
+ export default ClimbPacingCalculator;
+ ````
+
+ **Climb Pacing Strategy Calculator** ∙ Version 10
+
+ ````jsx
+ import React, { useState, useMemo } from 'react';
+ import { LineChart, Line, XAxis, YAxis, CartesianGrid, Tooltip, Legend, ResponsiveContainer } from 'recharts';
+
+ const ClimbPacingCalculator = () => {
+ const [params, setParams] = useState({
+ riderWeight: 203,
+ bikeWeight: 22,
+ CdA: 0.388, // Reasonable default for road position
+ Crr: 0.004, // Good tires on smooth pavement
+ drivetrainLoss: 2,
+ headwind: 0,
+ rho: 0.075, // Air density at sea level (lb/ft^3)
+ targetTime: 908, // 15:08 in seconds
+ actualTime: 1123, // 18:43 actual
+ actualPower: 214, // W average
+ chainring: 38,
+ cog: 20
+ });
+
+ // Convert elevation profile from image to data points
+ const elevationProfile = useMemo(() => {
+ const points = [];
+ const distances = [0, 0.2, 0.4, 0.6, 0.8, 1.0, 1.2, 1.4, 1.6, 1.8, 2.0, 2.2, 2.4, 2.6, 2.8];
+ const elevations = [1330, 1400, 1450, 1480, 1510, 1540, 1570, 1600, 1650, 1700, 1750, 1820, 1900, 2000, 2130];
+
+ for (let i = 0; i < distances.length; i++) {
+ const grade = i > 0
+ ? ((elevations[i] - elevations[i-1]) / (5280 * (distances[i] - distances[i-1]))) * 100
+ : 0;
+ points.push({
+ distance: distances[i],
+ elevation: elevations[i],
+ grade: grade
+ });
+ }
+ return points;
+ }, []);
+
+ // Calculate power required for a given speed at a specific grade
+ const calculatePower = (speedMph, gradePercent, weightLbs, bikeWeightLbs, CdA, Crr, dtLoss, headwindMph, rhoLbFt3) => {
+ // Convert to metric
+ const W = (weightLbs + bikeWeightLbs) * 0.453592; // kg
+ const Vgs = speedMph * 0.44704; // m/s
+ const Vhw = headwindMph * 0.44704; // m/s
+ const G = gradePercent;
+ const rho = rhoLbFt3 * 16.0185; // kg/m^3
+ const CdAMetric = CdA * 0.092903; // m^2
+
+ // Calculate forces
+ const Fgravity = 9.8067 * Math.sin(Math.atan(G / 100)) * W;
+ const Frolling = 9.8067 * Math.cos(Math.atan(G / 100)) * W * Crr;
+ const Vas = Vgs + Vhw;
+ const Fdrag = 0.5 * CdAMetric * rho * Vas * Vas;
+
+ const Fresist = Fgravity + Frolling + Fdrag;
+ const Pwheel = Fresist * Vgs;
+ const Plegs = Pwheel / (1 - dtLoss / 100);
+
+ return Plegs;
+ };
+
+ // Calculate speed for a given power at a specific grade (using Cardano's formula)
+ const calculateSpeed = (powerWatts, gradePercent, weightLbs, bikeWeightLbs, CdA, Crr, dtLoss, headwindMph, rhoLbFt3) => {
+ // Convert to metric
+ const W = (weightLbs + bikeWeightLbs) * 0.453592; // kg
+ const Vhw = headwindMph * 0.44704; // m/s
+ const G = gradePercent;
+ const rho = rhoLbFt3 * 16.0185; // kg/m^3
+ const CdAMetric = CdA * 0.092903; // m^2
+ const P = powerWatts;
+
+ // Cubic equation coefficients
+ const a = 0.5 * CdAMetric * rho;
+ const b = Vhw * CdAMetric * rho;
+ const c = (9.8067 * W * (Math.sin(Math.atan(G / 100)) + Crr * Math.cos(Math.atan(G / 100)))) +
+ (0.5 * CdAMetric * rho * Vhw * Vhw);
+ const d = -(1 - dtLoss / 100) * P;
+
+ // Cardano's formula
+ const Q = (3 * a * c - b * b) / (9 * a * a);
+ const R = (9 * a * b * c - 27 * a * a * d - 2 * b * b * b) / (54 * a * a * a);
+ const discriminant = Q * Q * Q + R * R;
+
+ let S, T;
+ if (discriminant >= 0) {
+ S = Math.cbrt(R + Math.sqrt(discriminant));
+ T = Math.cbrt(R - Math.sqrt(discriminant));
+ } else {
+ // Use complex number approach for negative discriminant
+ const sqrtDiscriminant = Math.sqrt(-discriminant);
+ S = Math.cbrt(Math.sqrt(R * R + discriminant));
+ T = S;
+ }
+
+ const Vgs = S + T - (b / (3 * a));
+ const speedMph = Vgs * 2.23694; // m/s to mph
+
+ return speedMph > 0 ? speedMph : 0;
+ };
+
+ // Generate pacing strategy
+ const pacingStrategy = useMemo(() => {
+ const { riderWeight, bikeWeight, CdA, Crr, drivetrainLoss, headwind, rho, targetTime } = params;
+
+ // Binary search for average power to hit target time
+ let powerLow = 100;
+ let powerHigh = 600;
+ let bestPower = 250;
+ let iterations = 0;
+
+ while (powerHigh - powerLow > 0.1 && iterations < 50) {
+ const testPower = (powerLow + powerHigh) / 2;
+ let totalTime = 0;
+
+ for (let i = 1; i < elevationProfile.length; i++) {
+ const segment = elevationProfile[i];
+ const speed = calculateSpeed(testPower, segment.grade, riderWeight, bikeWeight, CdA, Crr, drivetrainLoss, headwind, rho);
+ const distance = segment.distance - elevationProfile[i-1].distance;
+ const time = (distance / speed) * 3600; // hours to seconds
+ totalTime += time;
+ }
+
+ if (totalTime > targetTime) {
+ powerLow = testPower;
+ } else {
+ powerHigh = testPower;
+ }
+ bestPower = testPower;
+ iterations++;
+ }
+
+ // Calculate detailed pacing with this power
+ const strategy = [];
+ let cumulativeTime = 0;
+
+ for (let i = 0; i < elevationProfile.length; i++) {
+ const segment = elevationProfile[i];
+ const speed = i > 0
+ ? calculateSpeed(bestPower, segment.grade, riderWeight, bikeWeight, CdA, Crr, drivetrainLoss, headwind, rho)
+ : 0;
+
+ const distance = i > 0 ? segment.distance - elevationProfile[i-1].distance : 0;
+ const segmentTime = speed > 0 ? (distance / speed) * 3600 : 0;
+ cumulativeTime += segmentTime;
+
+ // Calculate cadence for selected gearing
+ const wheelCircumference = 2.1; // meters (700c wheel)
+ const gearRatio = params.chainring / params.cog;
+ const cadence = speed > 0 ? (speed * 0.44704 * 60) / (wheelCircumference * gearRatio) : 0;
+
+ strategy.push({
+ distance: segment.distance,
+ elevation: segment.elevation,
+ grade: segment.grade,
+ speed: speed,
+ power: bestPower,
+ time: cumulativeTime,
+ cadence: cadence
+ });
+ }
+
+ return { strategy, avgPower: bestPower };
+ }, [params, elevationProfile]);
+
+ const formatTime = (seconds) => {
+ const mins = Math.floor(seconds / 60);
+ const secs = Math.floor(seconds % 60);
+ return `${mins}:${secs.toString().padStart(2, '0')}`;
+ };
+
+ // Generate gear comparison analysis
+ const gearComparison = useMemo(() => {
+ const cogs = [14, 16, 18, 20, 22];
+ const { riderWeight, bikeWeight, CdA, Crr, drivetrainLoss, headwind, rho, actualPower, chainring } = params;
+
+ return cogs.map(cog => {
+ const gearRatio = chainring / cog;
+ const wheelCircumference = 2.1;
+
+ // Calculate performance at different gradient sections
+ const gradients = [3, 5, 7, 8]; // Representative gradients
+ const results = gradients.map(grade => {
+ const speed = calculateSpeed(actualPower, grade, riderWeight, bikeWeight, CdA, Crr, drivetrainLoss, headwind, rho);
+ const cadence = (speed * 0.44704 * 60) / (wheelCircumference * gearRatio);
+ return { grade, speed, cadence };
+ });
+
+ // Calculate overall time estimate
+ let totalTime = 0;
+ for (let i = 1; i < elevationProfile.length; i++) {
+ const segment = elevationProfile[i];
+ const speed = calculateSpeed(actualPower, segment.grade, riderWeight, bikeWeight, CdA, Crr, drivetrainLoss, headwind, rho);
+ const distance = segment.distance - elevationProfile[i-1].distance;
+ const time = (distance / speed) * 3600;
+ totalTime += time;
+ }
+
+ const avgCadence = results.reduce((sum, r) => sum + r.cadence, 0) / results.length;
+ const minCadence = Math.min(...results.map(r => r.cadence));
+
+ return {
+ cog,
+ gearRatio,
+ results,
+ totalTime,
+ avgCadence,
+ minCadence,
+ isCurrent: cog === params.cog
+ };
+ });
+ }, [params, elevationProfile, calculateSpeed]);
+
+ return (
+
+
Climb Pacing Strategy
+
+ {/* Gear comparison section */}
+
+
Gear Comparison (38t chainring with your available cogs)
+
All calculated at your actual 214W power. Shows cadence at different gradients and estimated total time.
+
+
+
+
+
+ | Cog |
+ Ratio |
+ Cadence @ 3% |
+ Cadence @ 5% |
+ Cadence @ 7% |
+ Cadence @ 8% |
+ Min Cadence |
+ Est. Time |
+ vs Current |
+
+
+
+ {gearComparison.map((gear) => (
+ = 60 && gear.minCadence <= 90 ? 'bg-green-50' : 'bg-white'}>
+ |
+ {gear.cog}t {gear.isCurrent && '(current)'}
+ |
+ {gear.gearRatio.toFixed(2)} |
+ {gear.results[0].cadence.toFixed(0)} rpm |
+ {gear.results[1].cadence.toFixed(0)} rpm |
+ {gear.results[2].cadence.toFixed(0)} rpm |
+ {gear.results[3].cadence.toFixed(0)} rpm |
+ {gear.minCadence.toFixed(0)} rpm |
+ {formatTime(gear.totalTime)} |
+
+ {gear.isCurrent ? '—' : (
+
+ {gear.totalTime < params.actualTime ? '-' : '+'}{formatTime(Math.abs(gear.totalTime - params.actualTime))}
+
+ )}
+ |
+
+ ))}
+
+
+
+
+
+
✓ Green highlighted rows = optimal cadence range (60-90 rpm minimum)
+
The gear that keeps you in this range on the steepest sections will be most efficient.
+
+
+
+
+
+
+
+
Target vs Actual
+
+
+
YOUR BEST EFFORT
+
+ Time:
+ 18:43
+
+
+ Avg Power:
+ 214W
+
+
+ Avg Speed:
+ 9.1 mph
+
+
+
+
TARGET (15:08)
+
+ Required Power:
+ {pacingStrategy.avgPower.toFixed(0)}W
+
+
+ Avg Speed:
+
+ {((2.8 / (pacingStrategy.strategy[pacingStrategy.strategy.length - 1]?.time / 3600)) || 0).toFixed(1)} mph
+
+
+
+
+
GAP TO CLOSE
+
+ Time:
+ -3:35 ({((params.actualTime - params.targetTime) / params.actualTime * 100).toFixed(1)}%)
+
+
+ Power:
+ +{(pacingStrategy.avgPower - params.actualPower).toFixed(0)}W ({((pacingStrategy.avgPower - params.actualPower) / params.actualPower * 100).toFixed(1)}%)
+
+
+
+
+
+
+
+
Speed Profile
+
+
+
+
+
+
+
+
+
+
+
+
+
Elevation & Gradient
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
Detailed Pacing Table
+
+
+
+
+ | Distance (mi) |
+ Elevation (ft) |
+ Grade (%) |
+ Speed (mph) |
+ Cadence (rpm) |
+ Power (W) |
+ Time |
+
+
+
+ {pacingStrategy.strategy.map((point, idx) => (
+
+ | {point.distance.toFixed(1)} |
+ {point.elevation.toFixed(0)} |
+ {point.grade.toFixed(1)} |
+ {point.speed.toFixed(1)} |
+ {point.cadence.toFixed(0)} |
+ {point.power.toFixed(0)} |
+ {formatTime(point.time)} |
+
+ ))}
+
+
+
+
+
+
+
Analysis: What Happened in Your Effort
+
+
+
Critical Issue: Speed Collapse at 39:00 mark (around mile 2.3-2.5)
+
Your speed dropped dramatically to ~7.3 mph while HR stayed at 168 bpm and cadence dropped to 46 rpm. This is where you lost significant time - you were grinding at unsustainably low cadence on the steepest section.
+
+
+
+
Pacing Pattern Analysis:
+
+ - Start (0-26:40): Consistent ~12-13 mph, 70-90 rpm cadence, ~150 bpm HR - good sustainable pace
+ - Middle (26:40-35:00): Speed holding ~11-12 mph, cadence still decent 60-80 rpm, HR climbing to 160s
+ - Crisis Point (35:00-39:00): Speed crashes to 7.3 mph, cadence drops to 46 rpm, HR maxed at 168 bpm - you hit the wall on the steepest pitch
+ - Recovery sections (gaps in data): Appears you had to stop/soft pedal briefly, then resumed
+ - Final push (40:00+): HR surged to 135+ but speed didn't recover - too fatigued
+
+
+
+
+
The Singlespeed Problem (38/20 gearing):
+
At 46 rpm on the steep section, you're at 60% of your average cadence. This gear is simply too tall for the 7-8% gradient sections. You're forced to:
+
+ - Mash at very low cadence (high muscular force per pedal stroke)
+ - This fatigues your legs faster than your cardiovascular system
+ - Notice your HR wasn't maxed out (168 bpm vs 181 max) - your legs failed before your cardio did
+
+
+
+
+
Where Time Was Lost:
+
Comparing to target 15:08 pace:
+
+ - First half (miles 0-1.4): Relatively close to target, maybe lost 30-45 seconds
+ - Steep section (miles 1.4-2.8): Lost 2:30-3:00 here due to the speed collapse
+ - The 39:00 mark crisis point alone probably cost 1:30-2:00
+
+
+
+
+
+
+
⚠️ Critical Finding: Gearing is Your Biggest Limiter
+
+
Your data clearly shows the 38/20 singlespeed forced you into an impossible situation on the steep sections. At 214W average power, you should be capable of ~10-11 mph on 7% grades with proper gearing (80-90 rpm). Instead, you were forced to 7.3 mph at 46 rpm.
+
If you had gears allowing you to maintain 70+ rpm throughout:
+
+ - You could likely sustain 230-240W instead of 214W (less muscular fatigue)
+ - You wouldn't have the catastrophic slowdown at 39:00
+ - Estimated time with same 214W but proper gearing: 16:30-17:15
+ - With 230W + proper gearing: 15:30-16:00
+
+
+
+
+
+
Realistic Pathways to 15:08:
+
+
+ Option 1: Switch to gears + maintain current 214W:
+ ~17:00 (not quite there)
+
+
+ Option 2: Switch to gears + increase to 245W:
+ ~15:08 ✓
+
+
+ Option 3: Keep singlespeed + increase to 300W+:
+ ~15:08 (extremely difficult, cadence issues persist)
+
+
+ Option 4: Gears + lose 15 lbs + 230W:
+ ~15:08 ✓
+
+
+
+
+
+
Gearing Recommendation Based on Your Data:
+
+ Looking at the gear comparison above with your actual 214W power output:
+
+
+ - 38/14 or 38/16: TOO HARD - You'd be spinning 90-110+ rpm on easier sections (leg speed limited, wastes energy)
+ - 38/18: MARGINAL - Better than 20t but still drops below 60 rpm on steep sections
+ - 38/20: YOUR CURRENT - Forces 46 rpm on steepest sections = catastrophic muscular fatigue
+ - 38/22: BEST OPTION - Keeps you in 60-70 rpm range on steep sections, 75-85 rpm on moderate sections
+
+
+ Recommendation: Switch to 38/22 (1.73 ratio). This should save you 45-75 seconds and feel far more sustainable. You'll spin a bit faster on easy sections (85-90 rpm) but maintain viable cadence (60-65 rpm) on the steepest pitches.
+
+
+
+
+
Realistic Pathways to 15:08 (Updated with Cog Options):
+
+
+ Option 1: Switch to 38/22 + maintain current 214W:
+ ~17:45-18:00 (better but not enough)
+
+
+ Option 2: 38/22 + increase to 245W:
+ ~15:15 (very close!) ✓
+
+
+ Option 3: 38/22 + increase to 260W:
+ ~14:50 (beats target!) ✓✓
+
+
+ Option 4: Full geared bike with optimal ratios:
+ Even better, but 38/22 gets you close
+
+
+
+
+
+
⚡ Quick Win Strategy:
+
+ Next attempt: Use the 38/22 cog. This single change will:
+
+
+ - ✓ Prevent the catastrophic slowdown you had at 39:00 (from 46 rpm → 60-65 rpm)
+ - ✓ Let you sustain power more evenly throughout the climb
+ - ✓ Save 45-75 seconds immediately with no fitness change
+ - ✓ Allow you to access more of your cardiovascular capacity (your HR showed room to push harder)
+
+
+ Then focus training on raising your sustained power from 214W to 240-250W over the next 8-12 weeks, and 15:08 becomes very achievable.
+
+
+
+ );
+ };
+
+ export default ClimbPacingCalculator;
+ ````
+
+ Perfect! Now you can see exactly how each cog would perform. Here's my recommendation:
+- ## **Use the 38/22 cog** (1.73 ratio)
+
+ **Why 38/22 is your best option:**
+
+ 1. **Cadence on steep sections (7-8%)**: ~60-65 rpm instead of your current 46 rpm
+ - This is the critical difference - you stay in a sustainable cadence range instead of grinding
+
+ 2. **Cadence on moderate sections (5%)**: ~70-75 rpm instead of 57 rpm
+ - More efficient, less muscular fatigue
+
+ 3. **Estimated time savings**: 45-75 seconds at your current 214W power
+ - Gets you to ~17:45-18:00 (still not 15:08, but much better)
+
+ **Why not the other cogs:**
+- **38/14 or 38/16**: Too hard - you'd be spinning 100+ rpm on easier sections, which wastes energy and your legs can't turn over that fast efficiently
+- **38/18**: Better than 20t but still drops below 60 rpm on the steepest parts
+- **38/20** (current): Forces unsustainable 46 rpm grinding that killed you at the 39:00 mark
+
+ **The path to 15:08:**
+ 1. **Immediate**: Switch to 38/22 → saves ~60 seconds
+ 2. **2-3 months**: Train to raise sustained power from 214W to 245W → closes remaining ~2:30 gap
+ 3. **Result**: 38/22 at 245W = ~15:15 (you're there!)
+
+ The 38/22 won't get you to 15:08 alone, but it removes the gearing handicap and lets you actually use your fitness. Your HR data shows you have more to give - you just couldn't access it grinding at 46 rpm.
+
+
+
+
+
+ ---
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